{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 频率主义与贝叶斯主义 IV：Python的贝叶斯工具"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*这个notebook出自[Pythonic Perambulations](http://jakevdp.github.io)的[博文](http://jakevdp.github.io/blog/2014/06/14/frequentism-and-bayesianism-4-bayesian-in-python/)。The content is BSD licensed.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*这个系列共4个部分：中文版[Part I](http://muxuezi.github.io/posts/frequentism-and-bayesianism-chs)  [Part II](http://muxuezi.github.io/posts/frequentism-and-bayesianism-chs-ii)  [Part III](http://muxuezi.github.io/posts/frequentism-and-bayesianism-chs-iii)  [Part IV](http://muxuezi.github.io/posts/frequentism-and-bayesianism-chs-iv)，英文版[Part I](http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bayesianism-a-practical-intro/)  [Part II](http://jakevdp.github.io/blog/2014/06/06/frequentism-and-bayesianism-2-when-results-differ/)  [Part III](http://jakevdp.github.io/blog/2014/06/12/frequentism-and-bayesianism-3-confidence-credibility/)  [Part IV](http://jakevdp.github.io/blog/2014/06/14/frequentism-and-bayesianism-4-bayesian-in-python/)*\n",
    "\n",
    "<!-- TEASER_END -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我之前花了一堆时间来分享这两种思想。\n",
    "\n",
    "- [频率主义与贝叶斯主义 I: 实用介绍](http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bayesianism-a-practical-intro/) ，论述了频率主义和贝叶斯主义在科学计算方面的差异，在简单问题的处理方面两者基本等价，会得到相同的点估计(point estimates)结果。\n",
    "- [频率主义 vs 贝叶斯主义 II：当结果不同时](http://jakevdp.github.io/blog/2014/06/06/frequentism-and-bayesianism-2-when-results-differ/)，进一步介绍两者的差异，尤其是处理冗余参数方面的差异。\n",
    "- [频率主义 vs 贝叶斯主义 III：置信与可信，频率主义与科学，不能混为一谈](http://jakevdp.github.io/blog/2014/06/12/frequentism-and-bayesianism-3-confidence-credibility/)，介绍了频率主义置信区间与贝叶斯主义可信范围的差异，指出在科学研究中频率主义只会回答错误的问题。\n",
    "\n",
    "这一篇文章，我打算撇开哪些争论，谈谈Python实现贝叶斯研究的工具。\n",
    "现代贝叶斯主义的核心是[马尔可夫链蒙特卡罗算法，MCMC](http://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo)，样本后验分布(sample posterior distributions)的高效算法。\n",
    "\n",
    "下面我就用Python的三个包来演示MCMC:\n",
    "\n",
    "- [emcee](http://dan.iel.fm/emcee): the MCMC Hammer\n",
    "- [pymc](http://pymc-devs.github.io/pymc/): Bayesian Statistical Modeling in Python\n",
    "- [pystan](https://pystan.readthedocs.org/en/latest/): The Python Interface to Stan\n",
    "\n",
    "我不会太关心它们的性能，也不会比较各自的API。这篇文章也不是教程；这三个包都有很完整的文档和教程。我要做的是比较一下三者的用法。用一个相对简单的例子，演示三个包的解法，希望对你有所帮助。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 测试案例：线性拟合最优解"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为了解决问题，我们做一个三参数模型来找数据的线性拟合解。参数是斜率，截距和相关性(scatter about the line)；这个相关性可以当作冗余参数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "先来定义一些数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "np.random.seed(42)\n",
    "theta_true = (25, 0.5)\n",
    "xdata = 100 * np.random.random(20)\n",
    "ydata = theta_true[0] + theta_true[1] * xdata\n",
    "\n",
    "# add scatter to points\n",
    "xdata = np.random.normal(xdata, 10)\n",
    "ydata = np.random.normal(ydata, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0JJ2r52Yqu8y0JLXWczOVXWZaUpnleabyU4A7gfuAe4FaLN8OnABOAZPAtpTjWOAy05LU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\nSZIkSZKy9P9IrbyHX0e39QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ea3fdf1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xdata, ydata, 'ok')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "数据明显具有相关性，我们假设我们不知道误差。让我们构建一条直线来拟合。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型：斜率，截距和未知相关系数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由贝叶斯定义可得\n",
    "\n",
    "$$\n",
    "P(\\theta~|~D) \\propto P(D~|~\\theta) P(\\theta)\n",
    "$$\n",
    "\n",
    "其中，$D$表示观察数据，$\\theta$表示模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "假设线性模型有斜率$\\beta$，y轴截距$\\alpha$：\n",
    "\n",
    "$$\n",
    "\\hat{y}(x_i~|~\\alpha,\\beta) = \\alpha + \\beta x_i\n",
    "$$\n",
    "\n",
    "假设y轴坐标具有正态分布误差， 那么模型下的任何数据点的概率为：\n",
    "\n",
    "$$\n",
    "P(x_i, y_i~|~\\alpha, \\beta, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\left[\\frac{-[y_i - \\hat{y}(x_i~|~\\alpha, \\beta)]^2}{2\\sigma^2}\\right]\n",
    "$$\n",
    "\n",
    "其中，$\\sigma$是未知测量误差，为冗余参数。\n",
    "\n",
    "所以$i$的似然估计的乘积为：\n",
    "\n",
    "$$\n",
    "P(\\{x_i\\}, \\{y_i\\}~|~\\alpha, \\beta, \\sigma) \\propto (2\\pi\\sigma^2)^{-N/2} \\exp\\left[- \\frac{1}{2\\sigma^2} \\sum_{i-1}^N [y_i - \\hat{y}(x_i~|~\\alpha,\\beta)]^2\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 先验条件"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里我们比之前的更仔细地选择先验条件。我们可以简单的认为$\\alpha$，$\\beta$，和$\\sigma$都是flat priors(扁平先验)，但是我们必须记住**扁平先验并非都无信息先验(uninformative priors)!**Jeffreys先验可能是更好的选择，用对称的最大熵(symmetry and/or maximum entropy)来选择最大化的无信息先验(maximally noninformative priors)。虽然这种做法被频率论认为太主观，但是这么做是可以从信息理论中找到理论依据的。\n",
    "\n",
    "为什么flat prior可能产生坏的选择？看看斜率就明白了。让我们来演示一下斜率从0-10的直线变化情况；"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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q1CgUFhZCrVajpKQEIpGI3c9y4sQJdsiPfk2HvrtivFvWVMObqWlgzLTzbdu2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\nCRIkyPnk/wOq6WBV5NfJLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6e97103a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(subplot_kw=dict(aspect='equal'))\n",
    "x = np.linspace(-1, 1)\n",
    "\n",
    "for slope in np.arange(0, 10, 0.1):\n",
    "    plt.plot(x, slope * x, '-k')\n",
    "\n",
    "ax.axis([-1, 1, -1, 1], aspect='equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这些线按0.1的斜率间隔进行分布，高斜率区域的线十分密集。因为是扁平先验，你肯定会认为这些斜率彼此无差异。由上面的密集区域显然可以看出，斜率的扁平先验满足那些很陡的斜率。斜率的扁平先验不是一个最小化的无信息先验(minimally informative prior)，可能是最终使你的结果有偏差(尽管有足够多的数据，结果可能几乎是0)。\n",
    "\n",
    "你可能想动手做出一个更好的方案(可能在直线与x轴的夹角$\\theta$上用扁平先验)，但是我们有更严谨的方案。这个问题在贝叶斯文献中已经有了答案；我找到的最佳方案来自Jaynes的论文*直线拟合：贝叶斯方法(Straight Line Fitting: A Bayesian Solution)* [(pdf)](http://exordio.qfb.umich.mx/archivos%20pdf%20de%20trabajo%20umsnh/aphilosofia/bayesian%20importantes/leapz.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 斜率和截距的先验"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "假设模型为\n",
    "\n",
    "$$\n",
    "y = \\alpha + \\beta x\n",
    "$$\n",
    "\n",
    "那么构建参数空间(parameter-space)，其概率元素为$P(\\alpha, \\beta) ~d\\alpha ~d\\beta$\n",
    "\n",
    "因为$x$和$y$是对称的，我们就可以进行参数交互\n",
    "\n",
    "$$\n",
    "x = \\alpha^\\prime + \\beta^\\prime y\n",
    "$$\n",
    "\n",
    "其概率元素为$Q(\\alpha^\\prime, \\beta^\\prime)d\\alpha^\\prime d\\beta^\\prime$，由此可得\n",
    "\n",
    "$$\n",
    "(\\alpha^\\prime,~\\beta^\\prime) = (- \\beta^{-1}\\alpha,~\\beta^{-1}).\n",
    "$$\n",
    "\n",
    "通过雅可比变换(the Jacobian of the transformation)，可得\n",
    "\n",
    "$$\n",
    "Q(\\alpha^\\prime, \\beta^\\prime) = \\beta^3 P(\\alpha, \\beta).\n",
    "$$\n",
    "\n",
    "为了保持对称性，需要保证变量的改变不会影响先验概率，因此有：\n",
    "\n",
    "$$\n",
    "\\beta^3 P(\\alpha, \\beta) = P(- \\beta^{-1}\\alpha, \\beta^{-1}).\n",
    "$$\n",
    "\n",
    "此函数满足：\n",
    "\n",
    "$$\n",
    "P(\\alpha, \\beta) \\propto (1 + \\beta^2)^{-3/2}.\n",
    "$$\n",
    "\n",
    "即$\\alpha$服从均匀分布，$\\beta$服从参数为$\\sin\\theta$的均匀分布，其中，$\\theta = \\tan^{-1}\\beta$。\n",
    "\n",
    "你可能会奇怪，斜率的分布服从参数为$\\sin\\theta$的均匀分布，而非$\\theta$。$\\sin\\theta$可以被认为是源自截距。如果把变量$\\alpha$改为$\\alpha_\\perp = \\alpha\\cos\\theta$，那么均匀分布就变为$(\\alpha_\\perp,~\\theta)$。在用PyStan求解时我们会用这个。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\sigma$的先验"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "同理，我们希望$\\sigma$的先验与问题的规模变化无关(如，改变点的数据)。因此其概率必须满足\n",
    "\n",
    "$$\n",
    "P(\\sigma)d\\sigma = P(\\sigma / c)d\\sigma / c.\n",
    "$$\n",
    "\n",
    "方程等价于\n",
    "\n",
    "$$\n",
    "P(\\sigma) \\propto 1 / \\sigma.\n",
    "$$\n",
    "\n",
    "这就是Harold Jeffreys提出的[Jeffreys先验](http://en.wikipedia.org/wiki/Jeffreys_prior)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 把先验放一起"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "把它们放到一起，我们用这些对称性参数推导出模型的最小无信息先验：\n",
    "\n",
    "$$\n",
    "P(\\alpha, \\beta, \\sigma) \\propto \\frac{1}{\\sigma}(1 + \\beta^2)^{-3/2}\n",
    "$$\n",
    "\n",
    "综上所述，你可能用扁平先验做参数变换$(\\alpha, \\beta, \\sigma) \\to (\\alpha_\\perp, \\theta, \\log\\sigma)$，来解决这个问题，\n",
    "但我认为对称/最大熵(symmetry/maximum entropy)方法更简洁明了——而且让我们能看到三个Python包演示这个先验的内涵。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 用Python解决问题"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在有了数据，似然估计和先验，让我们用Python的emcee，PyMC和PyStan来演示。首先，让我们做一些辅助工作来可视化数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create some convenience routines for plotting\n",
    "\n",
    "def compute_sigma_level(trace1, trace2, nbins=20):\n",
    "    \"\"\"From a set of traces, bin by number of standard deviations\"\"\"\n",
    "    L, xbins, ybins = np.histogram2d(trace1, trace2, nbins)\n",
    "    L[L == 0] = 1E-16\n",
    "    logL = np.log(L)\n",
    "\n",
    "    shape = L.shape\n",
    "    L = L.ravel()\n",
    "\n",
    "    # obtain the indices to sort and unsort the flattened array\n",
    "    i_sort = np.argsort(L)[::-1]\n",
    "    i_unsort = np.argsort(i_sort)\n",
    "\n",
    "    L_cumsum = L[i_sort].cumsum()\n",
    "    L_cumsum /= L_cumsum[-1]\n",
    "    \n",
    "    xbins = 0.5 * (xbins[1:] + xbins[:-1])\n",
    "    ybins = 0.5 * (ybins[1:] + ybins[:-1])\n",
    "\n",
    "    return xbins, ybins, L_cumsum[i_unsort].reshape(shape)\n",
    "\n",
    "\n",
    "def plot_MCMC_trace(ax, xdata, ydata, trace, scatter=False, **kwargs):\n",
    "    \"\"\"Plot traces and contours\"\"\"\n",
    "    xbins, ybins, sigma = compute_sigma_level(trace[0], trace[1])\n",
    "    ax.contour(xbins, ybins, sigma.T, levels=[0.683, 0.955], **kwargs)\n",
    "    if scatter:\n",
    "        ax.plot(trace[0], trace[1], ',k', alpha=0.1)\n",
    "    ax.set_xlabel(r'$\\alpha$')\n",
    "    ax.set_ylabel(r'$\\beta$')\n",
    "    \n",
    "    \n",
    "def plot_MCMC_model(ax, xdata, ydata, trace):\n",
    "    \"\"\"Plot the linear model and 2sigma contours\"\"\"\n",
    "    ax.plot(xdata, ydata, 'ok')\n",
    "\n",
    "    alpha, beta = trace[:2]\n",
    "    xfit = np.linspace(-20, 120, 10)\n",
    "    yfit = alpha[:, None] + beta[:, None] * xfit\n",
    "    mu = yfit.mean(0)\n",
    "    sig = 2 * yfit.std(0)\n",
    "\n",
    "    ax.plot(xfit, mu, '-k')\n",
    "    ax.fill_between(xfit, mu - sig, mu + sig, color='lightgray')\n",
    "\n",
    "    ax.set_xlabel('x')\n",
    "    ax.set_ylabel('y')\n",
    "\n",
    "\n",
    "def plot_MCMC_results(xdata, ydata, trace, colors='k'):\n",
    "    \"\"\"Plot both the trace and the model together\"\"\"\n",
    "    fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "    plot_MCMC_trace(ax[0], xdata, ydata, trace, True, colors=colors)\n",
    "    plot_MCMC_model(ax[1], xdata, ydata, trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "下面，就让我们来解决MCMC。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Emcee"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[emcee](http://dan.iel.fm/emcee/current/)(就是Python历史上著名的MCMC Hammer)是天文学家[Dan Foreman-Mackey](http://dan.iel.fm/)写的纯Python包。这个简洁的包实现了复杂的仿射无关哈密顿(Affine-invariant Hamiltonian)MCMC。因为是纯Python，所以包很容易安装：\n",
    "\n",
    "```\n",
    "[~]$ pip install emcee\n",
    "```\n",
    "Emcee没有很多引用代码；只要传入Python函数就会返回与对数后验概率匹配的值和后验样本。下面用``emcee``演示一下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1.0\n"
     ]
    }
   ],
   "source": [
    "import emcee\n",
    "print(emcee.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Define our posterior using Python functions\n",
    "# for clarity, I've separated-out the prior and likelihood\n",
    "# but this is not necessary. Note that emcee requires log-posterior\n",
    "\n",
    "# 用Python函数定义后验，我把先验和似然估计分开写了，其实没必要，主要是显得更简洁。\n",
    "# 注意emcee需要对数后验证\n",
    "\n",
    "def log_prior(theta):\n",
    "    alpha, beta, sigma = theta\n",
    "    if sigma < 0:\n",
    "        return -np.inf  # log(0)\n",
    "    else:\n",
    "        return -1.5 * np.log(1 + beta ** 2) - np.log(sigma)\n",
    "\n",
    "def log_likelihood(theta, x, y):\n",
    "    alpha, beta, sigma = theta\n",
    "    y_model = alpha + beta * x\n",
    "    return -0.5 * np.sum(np.log(2 * np.pi * sigma ** 2) + (y - y_model) ** 2 / sigma ** 2)\n",
    "\n",
    "def log_posterior(theta, x, y):\n",
    "    return log_prior(theta) + log_likelihood(theta, x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Here we'll set up the computation. emcee combines multiple \"walkers\",\n",
    "# each of which is its own MCMC chain. The number of trace results will\n",
    "# be nwalkers * nsteps\n",
    "\n",
    "# 设置计算参数。emcee组合了多个\"walkers\"，每个都有自己的MCMC链。\n",
    "# 跟踪结果的数量为nwalkers * nsteps\n",
    "\n",
    "ndim = 3  # number of parameters in the model\n",
    "nwalkers = 50  # number of MCMC walkers\n",
    "nburn = 1000  # \"burn-in\" period to let chains stabilize\n",
    "nsteps = 2000  # number of MCMC steps to take\n",
    "\n",
    "# set theta near the maximum likelihood, with \n",
    "np.random.seed(0)\n",
    "starting_guesses = np.random.random((nwalkers, ndim))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4.38 s, sys: 1.09 ms, total: 4.38 s\n",
      "Wall time: 4.38 s\n",
      "done\n"
     ]
    }
   ],
   "source": [
    "# Here's the function call where all the work happens:\n",
    "# we'll time it using IPython's %time magic\n",
    "\n",
    "# 这就是所有调用内容。\n",
    "# 这里用IPythn的%time方法计时。\n",
    "\n",
    "sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[xdata, ydata])\n",
    "%time sampler.run_mcmc(starting_guesses, nsteps)\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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6upq8vDzq6+ubZXQeOXKE6Oho6urqsLKyIigoqF0iraCggMjISP71r3/x/PPP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\nRERERERERGS2+X8A0fnNC5wm3wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6e971e1c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sampler.chain is of shape (nwalkers, nsteps, ndim)\n",
    "# we'll throw-out the burn-in points and reshape:\n",
    "\n",
    "# sampler.chain返回数组维度为(nwalkers, nsteps, ndim)\n",
    "\n",
    "sampler.chain\n",
    "emcee_trace = sampler.chain[:, nburn:, :].reshape(-1, ndim).T\n",
    "plot_MCMC_results(xdata, ydata, emcee_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "左图，我们演示了由冗余参数$\\sigma$边缘化后的跟踪结果。在右侧显示了2-$\\sigma$最佳拟合的不确定区域。这就是我们从MCMC得到的结果：边缘化的不确定轮廓提供了一个很好的拟合结果。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyMC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[PyMC](http://pymc-devs.github.io/pymc/)包比emcee有更多的特征，有效的支持许多主流先验分布。\n",
    "PyMC默认使用经典的[Metropolis-Hastings](http://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm)取样器，最早的MCMC算法。性能方面，使用了Fortran库，因此用pip安装就有点复杂。先安装Fortran编译器，``pip install pymc``可以了。如果没装Fortran编译器，可以通过[conda](https://conda.binstar.org/pymc)安装。\n",
    "\n",
    "据说[PyMC第三版](https://github.com/pymc-devs/pymc)要移除Fortran依赖，安装就容易了。而且PyMC 3的API更简洁，性能更好。但是目前仍是alpha版本，所以现在用就版本："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.3.3\n"
     ]
    }
   ],
   "source": [
    "import pymc\n",
    "print(pymc.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Define the variables needed for the routine, with their prior distributions\n",
    "alpha = pymc.Uniform('alpha', -100, 100)\n",
    "\n",
    "@pymc.stochastic(observed=False)\n",
    "def beta(value=0):\n",
    "    return -1.5 * np.log(1 + value ** 2)\n",
    "\n",
    "@pymc.stochastic(observed=False)\n",
    "def sigma(value=1):\n",
    "    return -np.log(abs(value))\n",
    "\n",
    "# Define the form of the model and likelihood\n",
    "@pymc.deterministic\n",
    "def y_model(x=xdata, alpha=alpha, beta=beta):\n",
    "    return alpha + beta * x\n",
    "\n",
    "y = pymc.Normal('y', mu=y_model, tau=1. / sigma ** 2, observed=True, value=ydata)\n",
    "\n",
    "# package the full model in a dictionary\n",
    "model1 = dict(alpha=alpha, beta=beta, sigma=sigma,\n",
    "              y_model=y_model, y=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 100000 of 100000 complete in 55.8 sec"
     ]
    }
   ],
   "source": [
    "# run the basic MCMC: we'll do 100000 iterations to match emcee above\n",
    "S = pymc.MCMC(model1)\n",
    "S.sample(iter=100000, burn=50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6nY6dO3cSGRnZKuWonAPnx2ls2LCBsWPHEh0dTXp6OgEBtjrpgoIC4uLiyMnJ\n4cCBA9TU1HDixAlmzJjBxIkT1Rq0vLw8dX2VlZXodDoqKyspLi7Gz89Pjb4prwFU0W3fjKCkZH/6\n6Se2bNnCtm3beOGFF1i6dGmn7oXg+jhh6vNKkf3LxUhKSiIhIYH8/Hz12KhRo1i7di2zZs26LBHX\n2XObmpo4ffo0ZrPZ4QLtxIkTrF692qlN093c3NBoNAQEBBAQEODSnqHgOqnPw9hSm1cDJcCD2JoJ\n7NkOvI0tfeCNLTX6Vs8t0bVpK0raRpr0ej1btmzBzc2NiIgIALXgX+nGVAbVKihNA0qHpvIzpZEg\nMTGRBQsWsGfPHiZNmkRAQAB79uzhxIkT3HDDDWodW01NDZMmTaKwsBB/f3/Gjh1LYWEhhYWF3HHH\nHWqzgslkUuet6fV6Nm7cSHh4uLoeHx8fXn31Va655hr+8Ic/8O233/KrX/2K0aNHtxKonZ21JgiC\ncCnWrVvXSqQB5Ofns379eoALRJzyuK0Aa0/wtT3XYrFgMpk4c+aMwwVaW9P0//7v/3YqAaSkMf39\n/QkMDESr1TplhK+n6cnkbjO21vUU4Cg2m5VjwNPnvsA2LHI38D3wL2yziY724BpdFmVOmhIRUyJK\n9s9DQkKIiorid7/7HVOnTmX//v2ATdDNnTuXkJAQYmJiiIqKUuelgW0OWl5eHpWVlWzfvh2TycSG\nDRuoqKggODhYFVfJyclkZmaSnZ3NyJG2OaCVlZUYjUYSEhI4ePAgZrOZ4uJioqOj1UJVk8mkijRF\nLCoiMC4uTk1tKwIOYNGiRWzdupWhQ4cyZ84cfv/733Py5EmAC0Rae/PlLnUvBUEQFBoaGto9Xl9f\nf0kRZ8+lzjWbzeTm5jpcpJnNZtauXct9992Hv78/X375JfPmzXMKkabMOxs4cCDDhw8nMjKS4cOH\n95hjgCvQ01V4ycA1QATwh3PH3j/3pfDf2LzzooB1Pbo6F0ZpImhrxq6IraysLLXu64EHHuD+++9n\nzZo1nD59GoB33nmHjIwMQkJCMBgMBAcHYzAYqKioIDY2Vk1Pjh07FgA/Pz8qKyvx8/OjoKCASZMm\nqT+Ljo4mOzub3bt3M3HiRAYMGEB6ejqxsbH4+fkxe/ZsNWXp7+9PQUEBmzdvVtdZUVFBRUUF0dHR\nJCcnYzAYyMrKUsWjwWCgpKSEmpoa1q1bR2JiIj/++COPPvooFRUVF0TSLjeidiXiThCEvktHgsbH\nx+eiIq7dRAmlAAAgAElEQVQtHZ1bW1tLQUGBwzs6Gxsb+fjjj/n5z39OWVkZn3/+OS+88AKDBg1y\nyPW7gkajwdvbG71e79LDaHsCV5WrUuPBlRXIK3Vr3377Lffffz9vv/02+/fvV8dpKKlQe4GnjOlI\nT08HaDUPLTg4mISEBLy9vWloaECv1xMcHExoaCi5ubmYTCa0Wi0DBgyguLhY7Qq9/fbbqa6u5sSJ\nE2r0bdy4cRw4cAA/Pz/18ZQpU9R6ODhvP6WkalNTU5k7dy5FRUW89dZb7N69m507dzJq1KhuMXkX\neg+pURN6i4vVqK1bt46vvvrqgtfExsaye/fuC461d+6tt97Ke++957D1Oqtpuv28s8DAQHx8fHp5\nRT2Hq9SoCQ6ms12N9iM49Ho9JSUlTJgwgSeeeIJdu3bxzjvvAOedCIxGo+rlqTQaGI1GdS7a7Nmz\nAZtjweHDh5k8ebIasg8ODsbPz4/09HSqqqoYNGgQFRUVxMfH8+abbzJmzBi0Wi3h4eEkJiYSHByM\nv78/R44cwWw2A+cFm9IdqtPpWnmI6vV6jEYjWVlZas3c0aNHefnllxk6dCi33nor27ZtY9SoUd1w\n1wVB6G8o9WPr16+nvr4eHx8fFi9erB7Pz8+/QMQtXrz4gussWbLkgnOvuuoqHn64bbn2lWNvmr5y\n5Upuuqm9xuSew95nMygoiIEDB0pK8zJx1bsln0jt6Mgqqj0hZ/+9qamJCRMmcOjQIXJzc9X5ZZs3\nb25l82Q/+DYnJ4fMzEzAVvegdIT+4Q9/4IYbbqC6uhqz2UxWVhZms5knn3yS5ORkCgoK+PnPf052\ndjZHjx7liSee4MiRIxw9ehRPT0+efPJJ/vznP7N06VI2b95MWFgYY8eOJTk5Wd3wlEhaQUEB8+fP\nVwfwwvkZcFFRUezbt4+EhATeeustHn300Q47QCXi5lpIRE1wVpKSkjoUcW1JTExk9erV1NXV4eXl\nxdy5c5k2bVqX1+Bspun9faRGW1zFQsqRyEZ3GbQdeGs/ruOll17iV7/6Fffff/8Fr1PqxhRXAcUT\n1Gg0smfPHsaNG0dBQQETJ05Uzx0zZoyaIq2qqsJsNtPU1KSO3zh16hRPPvkk2dnZFBYWcubMGYYM\nGQLYhhjW1dWh1Wq54YYbmDhxInv27MFgMDBmzBh1blplZSXz588HWgs0+5Ttjh07WLVqFY888ghP\nP/00w4cPB1pHFzsj4ATnQYSa4Mq0tLRgMBiorKx0aKNAUVER69ev59ChQzzzzDPMmTMHT09Ph13/\nclBSm4MGDVK7NgUbItQElfZEhjKuQsFerH388cd8/PHHfPPNN60EXNtUo1Krpgy0DQgIIDExkQED\nBuDr64ufnx9ms5mamhoA0tPTmT59Ovv27VPHawQFBZGZmcm4ceM4duwYNTU1TJs2jbS0NCZPnkxh\nYSGnTp1i6dKlFBQUUF1dzd69e5k9e7Y6dy07O5sPPviA1NRUtUZNGR8SHBysNhvo9XrKysp48MEH\nGT16NE888YSasm3vfsncNedHhJrgilitVsrLyyktLcVqtTpMpDnSNH3fvn1s3ryZxsbGy47y2bsF\nBAUF4efnJw0B7dCV/UvuZj9g/PjxF3RAKt9HjhzJt99+y9dff60KFvvOUXuRFh0dTVBQEBEREWRm\nZjJy5EgmTZpETU0NZrMZo9FIbW0tx44dY9y4cQB4enpSUFBAVVUVYOsWjY2NpaamhmHDhnH48GEA\n/v73v1NWVkZVVRXffPMNx44dIy0tjZUrV7Jt2zb8/Pw4ceIEQUFBJCYmqlZXYKufU9K2iYmJ6vp/\n9rOf8eGHHzJw4EBef/11MjMzL+jmtL8fvSHSpLtUEPoutbW1HD9+HIPBgMVicYhIq62t5YMPPmD2\n7NlYLBa2b9/Os88+2yWRtmrVKtLS0jh8+DBpaWmsWrWKffv2XfR1SmpzyJAhjBkzhpEjRzJo0KAe\nF2lJSUnExsYSExNDbGwsSUlJPfr+PYGrfjqVT6RXSHsRt8cee4wRI0bw+uuvq+eAreMzNjaWkpKS\nVlY+QUFBmEwmNe1pMpl49913mTx5MidOnKCiooLbb7+dI0eOkJmZybx58yguLuabb76huroad3d3\nvL298fX1paSkBHd3d+rr6zGbzQQEBNDc3ExDQwNjxoxh6tSpHD58GH9/fwoLC1mxYoXqeFBYWEhC\nQkIrQ3ilCzQlJUUVl1arlR07dvDRRx+xY8cOrr/++naN3SXl6dxIRE1wFbrDVaC7TNOffvpp0tLS\nLjg+efJk3n///VbHFCN0+9Rmb9bBXcoxwpmQrk+hXTryu7Sv0wL4+c9/zhtvvMFTTz2FRqNRbaWC\ng4NV0WbvTqCkRIOCgtQCWr1ej7+/PydPnuT2228nNzeXiooKpk+fTnp6Onl5eTQ2NqLRaKiurubs\n2bMADBw4EE9PT8aNG4fJZOLs2bPo9Xqqq6v58ccfqampQavVMmLECMaMGcOBAwcIDQ0lPDxcTb8W\nFxcDqP6jKSkpqqG78nsOGzaMuro6pk6dqhq720fR2t4T5X6BpEMFQegcFouFsrIyjEajwwSaYpq+\nZs0ahgwZ4nDT9MbGxoseV4SYj48PQUFBTjXr7GIDhJ1NqHUF57jbQrfQ1oxded5WkFx99dVUVlby\nj3/8Q3UvCAkJwWg0qq/JyckhKipKdQ9Q0o3R0dG8/PLLAFRXVzNx4kS+/fZb1bcT4PDhw/z4448U\nFxfT2NhIYGAgQ4YM4c4772TOnDnodDp11IZer2fIkCFERUWh1WopKSnh5MmTHDhwgJMnT5KWloZO\np+PNN9+koqKCxMREdX3V1dXodDrVX1SJBiq//6pVq9i5cyf/8R//wZ///GfKysqA9kVa23soCIJw\nMZQRRY4Uad999x2//OUveeedd1i6dCkbNmxwqEgD8PLyave4t7c3Hh4eBAcHM2bMGEaNGoVOp3Ma\nkQYXd4zoSzjPHRe6jfbEhiJeSkpKmDhxIhs2bOCll16itLRUPR4VFaVaUEVGRqrpz6eeeoqoqChK\nSkrIzc0lLy9PrXXLysoiICAArVZLaGgoWVlZ6PV6dDod4eHhjBo1ipiYGIYNG4aPjw+HDx+msrKS\nwMBAsrOzyc3NpaCggIqKCoYPH84111zD8OHDMZlMfP3115w9e5bPPvuM0aNHc/DgQcaMGcNrr73G\ngQMHVIN3ZZQI2Izd7aNmWq2Wd999F09PTyZPnkx+fn6rRov2OmQFQRA6oqGhweGuAidOnGDx4sUs\nW7aMBx54gG3btjF16tRuSTPOnTuXq666qtWxsLAwnnvuOa655hqGDBnSa12kl+JijhF9CVet95Aa\nj24gISGBY8eOsXv3btVXU5mlpmAymcjMzFQ7K8eNG6fWjCnm67W1tcTHx5OYmMjx48cpKSmhtraW\nW265hRMnTlBbW0ttbS1XXXUVdXV1+Pv7q9dTbKvc3d2ZPHkyp0+fxtPTEy8vLxoaGqipqeGnn34i\nMjKSiIgI7rrrLiorKwkPDyczM5M77rhDHSWisHDhQnU2nEJISAivvvoq77//PuvWreO6665rN/V5\nsVl0Qs8iNWqCM2GxWDhz5gwmk8lhEbS2pukPPfRQj/hx7t+/ny1bttDS0oKfnx9LlixxidRhf6lR\nc9VNTza6LtKe2Dh06BBPPfUU999/P3FxcRiNRtWZICQkhJSUFPbs2aMWsAYEBAAQExPD2rVrW4kt\nk8lEVVUV3t7eHD16lKCgIEaMGMGZM2fIy8tDq9Vy7bXX8sMPP1BdXY2Hhwdubm64ubnR2NiIxWJB\nr9fj4eFBc3MzANdddx1VVVWUl5djMBioq6vDarVy6623cu+991JUVITZbGbKlCmqV6gytkP5DrbU\nrzL37fTp06xcuZK//e1vzJgxo1PDg4XeQYSa4AxYrVaqqqo4ffq0wzo5zWYzH374Idu2bWPOnDk8\n8cQTPeLHqdFo0Gq1BAcHu6xjwOUMG+5NRKgJDqGkpASr1cqECRP405/+xC233KJG1hShM378+FZd\noMpMtcjISJKTk9m7dy+hoaGcOHGCqKgojEYjBw8eVD0/wVYTMXLkSLKzsxk4cCA+Pj4UFRXh7e2N\nm5sbY8eOJSsri/r6ekaNGoXZbKaxsZGgoCCampoICwujoaGBoqIi/Pz8VOEXGxtLQEAAWVlZrF27\nluTkZHUY76RJk1S/0ujoaFVQjh8/nrfeeovf/OY3rFy5kueff169FyLOnIsuCrUlwCdAhcMWdOXI\n/uWCWK1WzGYzpaWlNDY2OkSgNTY28re//Y2//OUv3HbbbSxcuLBVKUZ3oNFo0Gg0BAQEEBQU1GGN\nmuBYurvr8xngZuAU8AHwIFAOfHHuu+CCdJTGCw0N5a9//SsLFizgu+++azWjDFCH4QYFBbFnzx4e\nfPBBjEYjycnJ6HQ6JkyYgMFgoLy8XDVmLy0t5eabb+bo0aO4u7szcuRITpw4gVarxWg04u3tzbBh\nwygvL8fLy0utk/Pw8CA/Px8PDw/10+VPP/3EmTNnAFttxfbt25k/fz7ffvstn3/+OaGhoTzwwANs\n3bqVsLAwTCYTY8aMITs7m4iICKKjo8nJyQHON1XExMSwa9cu5s2bR01NDb/+9a+7lOKUFKlTMhQ4\nBGQAHwIpgKgl4ZJYrVaqq6sxGAy0tLRgsVi6fM22pukbNmzodtN0Ze5ZcHBwr8w7E66czqi7OCAZ\nGAX8AfjLucczgDeAw922uo6RT6RdoDPpvFdffZXvvvuOhIQE4uLiKCkpISsrS00fKoNwo6KiyMrK\nwmQykZiYSExMDImJiUyYMIGwsDASExPJzs5m6NChGI1GRo4cSVZWFm5ubmqEraWlhZaWFqqqqhg4\ncCBarRZfX1+KiooYNGgQQUFBqrBzd3enrq6OlpYWoqKiGDFihGo7pUThKisrmTlzJmPHjuXIkSPE\nxMSoadoDBw7w2muvqdZThw8fZuLEicTGxrJlyxZWrFjB7bffzttvv93vvemcDQekPt2Au4HHgInA\nZ9j2s/yLvKY76Pf7V1JSEuvWraOhoQFvb2+nrIlSUpylpaUOE2jQ2jT9ueee61bTdCWV6efnx+DB\ng694KK7Qdbo79TkHW/TMArwG/NbutQnAmit54y7S7zc6R9M2CrRr1y5+//vfc9ttt7Fo0aILhsJm\nZGSQk5NDRUUFhYWFhIWFERERwZ49ezCbza2uvWXLFiwWC0OHDsXT05Nhw4bxww8/UFlZSVNTE56e\nnvj4+FBfX4+fnx8mkwl/f388PT2pq6vDYrHQ0tLCiBEjKCwsZMiQIRiNRoYNG8aZM2e48cYbaWho\nYMiQIZw5cwar1UpmZibXXXcd48aNQ6/XYzabCQ0NRafTqY0OSneoff1aREQE999/Pw0NDXz44Ydo\ntdrLiopJFK37cFCN2g3AfGwfNPcAtwDfAC938bqXQ7/ev5y9ANxisVBZWUlpaanDatCgZ0zT21pB\nLVy4kF/84hfyodMJ6G6h5gPcAxRgSx3YMwf4+5W8cRfp1xtdd2Iv2IqLi4mNjeXLL79kypQpwHnf\nUCW6pniCKhQUFLB3714mTJiAv78/ubm5bN26lenTp6uzbZT5ZUajUY2m1dXV4eHhgcViwdvbm5qa\nGpqbm2lubsbb25vGxkbc3Nzw9vamoaGBYcOGUV1dTWBgoOpoUF1dTWxsLIcPH2bw4MH88MMPDB8+\nnJCQENXmRKfTERERoXaGRkREAKjp3YyMDAIDA1m4cCEGg4GPPvqIwMBAgFbDgi8myESsdQ9dFGoJ\nwC8BE7ABSASasEXZjmPLEvQU/Xr/io2N5auvvmr3+O7du3thRTYsFgvl5eUYjUaHCrRTp06xbt26\nbjdNV6ygioqK1GPOJID7O93t9VmPLUVwCpgJzMIm3JYAVVfypkLvYj8bTJmTpmDvfXnTTTexadMm\nHnzwQX744QdSUlIYP348qampajdocHAwFRW2+uygoCB0Op1aE6bT6aitrcXd3Z0jR45w7NgxGhoa\naGpqora2FrPZTGVlJS0tLer4DYvFwtmzZ1W3A+WToJ+fH1qtFi8vL4KCgjh9+jTNzc0YDAYCAgIY\nM2YM9fX1fPbZZ+r5t9xyCzqdjm+++YasrCzS09PJzs4mLy+P5ORkCgsLCQ4OJjg4mM2bN1NSUoLR\naMTLy4s33niDyZMnc9999/Htt992OCy47f1U7p3MX3M6ArF9sLwb237WdO64Bfi33lpUf8TZhpS2\ntLRgNBrJyclR05yOEGnl5eWsWrWKhx9+mPDwcJKSknjwwQcdLtKUbvlt27a1Emlwfkq/4NpcTjz0\n9LkvBR1wIzbxZgF676OQcFnYpzg7msgPNgEyc+ZMZs+ezbJly9ixYwcpKSnExMSo9kspKSksXLiQ\nkpISNm7ciE6nU0XVwYMHqaurw8vLi2nTplFYWMjIkSNpaGhQU5uenp7k5OTg5eWFVqulvr5e7agq\nKSmhpaUFNzc31dTd3d2dwYMHqzVudXV11NfXk5aWRm1tLcOHDycwMJDvv/+ehx9+mOzsbGbOnMnB\ngwc5ffo0QUFBVFZWsnv3bl577TXS09OprKxEp9OpPqHKPRo2bBgDBgzgySefZNeuXej1elWw2Q/S\nbW/WmkTUnI7lF/nZ0R5bheA0Q0pbWlooKytT56A5KoJWW1vLpk2b+OSTT4iLi+OLL74gKCjIIde2\np21zQEf0tSn9/ZGuJK4rgb2OWojQs7QnLjo6Z+3atURHR7NixQreeOMNMjIyMBgMavekYoAOkJ2d\nzZQpU7jjjjvYvHkz0dHR7N+/H7Bt0P/4xz/QarU0NjaqIzm8vLzQ6XRUVlbS3NyMRqNR56f5+Pi0\n2kCVpgN/f381PVpWVoaHhwc+Pj6cPn2ahoYGzGYzZrOZ+vp6cnNzufbaaykoKFAH3+r1ejZs2MAN\nN9xAeHg4YIsIKqNHIiMjAdsQ4DFjxjBjxgx27typrkMspwThyliyZAn5+fkX1KgtXry4R95f2TOU\nkg1HmqZ/8cUXvPvuu9x44418+umnDjFNt+dizQHOIoAFxyMVhn2czoyKuJRoMxqNvPjii/z2t7+l\npqaGP/7xj+px+xSoUrumPE9ISCA5OZkRI0Zw7NgxQkJCGDlyJAEBARgMBiIjI6mpqcFkMqkjOby8\nvNQBt76+vtTU1LRKf5rNZvXnFouFwMBAtc7Ny8uL2tpawJYO+Oabb2hubmbMmDFUV1ej0Wh44YUX\nWL9+PWFhYSxbtoxx48aRnp5OYWEh/v7+mEwm5s6dqwq6rKws4uLi0Ol0PPzww3z22WdMmDCh3Xvc\n0f0TBOE8Sr1UTw8pbWpqwmg0qqUajjZNX7t2LcHBwQ43TQfbfqbRaAgKCiIwMLDd5oDeFsBC9yED\nb4V2se/uVKJH//d//8e9997L/v37ufbaawFbNC02NpbNmzer4X1lVEd8fDwFBQV4eXnxm9/8hkmT\nJqmOA5mZmURHR3PixAlycnLw8/NTB+66ubnR0tKiDma0WCw0NTWpwg1sgs5qteLl5UV9fT0eHh7q\np82BAwfi7u7O6NGj1flpSkeoYjeVnZ1NeHg4999/P2fPngUgLi5Onb+mNBwA6gDKTZs2sXr1arZu\n3cptt912WaJMBFzXEWcCoT0uNeqjsbERo9FIZWUl4DiBBjbT9Lfeeouamhqef/55pkyZ4tBOTjc3\nNzw9PRk6dCh+fn6XvLarTOnvj4gzgdAhVyIQ2nuNUhz/7LPPcsMNNzB79mzAlgJMSUkBUGeq5eXl\nER8fT1ZWFtu3byc0NJRt27ZRVlbGnXfeybFjx7j22mvJzMykuroarVZLZWUlvr6+VFdXU1FRgbe3\nN/X19VgsFrUTtL6+Hk9PT5qabHXg7u7uqqBTCnR9fX2pqKhg9OjRVFdXc/bsWYYMGYKHhwdhYWFk\nZmYSEBBAVFQUR44coaWlhbi4OIqKioiLi1O7QJW0yNy5c1vNndu4cSPLli0jKSmJm2666YKIpQiy\n7kOEmtCWi436uOuuuygtLaW6utqh4gxspulr1qwhJyeHRYsWMWvWLNzd3R12fY1Gg5eXF3q93mWt\nnYTWdHfXp+DCtOdb2REdDcK1L5B/5ZVXWL16dat6iKioKKKiokhNTSU2NpaIiAg2btxIXl4eU6ZM\nITw8nJtuuony8vJWG051dTWhoaFqMX9ZWRn+/v54e3vT1NTEgAEDcHNzU6NmcL7eQmlEcHd3VzdI\nZSClEp1T2uy1Wi2enp7k5uYCEB0dzcCBA/nZz35GQ0MDhw8f5vXXX+fgwYMcPmyb36ykR1JSUsjK\nylKttMaNG8eqVauYMWMGX3/9dauGgpKSEvW89u61dIIKgmNZt25dK5EGtk7HN998k+PHj1NVVeVQ\nkXbmzBlWrFjB/PnzmTBhAjt27OCee+5xmEhTRhApUf3ORNGEvo8ItX7EpSI9F/u5IjKio6N56KGH\neP/999Hr9WRkZBASEqIW4CvjPuLi4li4cCFBQUEUFBRwww03MGfOHL755htV5L344os0NDSg0+kA\n0Ol06HQ6tf5CEWJKCtTT05Pa2lp8fHxoamqivr5ebaVXNjNFYDU2NhIYGIi/vz+BgYEUFxfT2NhI\nTEwM33zzDbW1tXh4eHDzzTeTn5/PggUL8PX1Zf78+eTl5amRNQWj0ag+9vb25s033+Thhx/m3Xff\nBc6POblYF62M7RAEx9LRqI/a2lqHCjSz2cy6deuYM2cO/v7+fPnll8ybN6/DAv7LRaPR4OPjIwJN\naBdpJujjdDUVZ1+rplxnwYIFxMbG8pvf/EY9T+mSBFvaUJlNVlBQwMSJEzGZTNx55538z//8D8OG\nDePYsWNqelERXWATWBaLhSVLlrBp0yY0Go064qOpqQmr1UpLSwuAOvxWsXdRNmaz2YyHhweVlZXq\nXLZBgwbh6+tLWloaLS0tnDx5En9/f3x8fJgyZQoHDhzAbDbj5+cH2LpXAWbPnq02TPzud79j/vz5\ngK1ubcSIETz22GNYLBYWLlx4wT1rL0LZUbTSEX9WgtDf6EgoOcpovLGxka1bt7JhwwZuu+02Pv/8\nc4eapms0Gry9vdHr9fj6+oo4E9rFVf9WSI1HJ+mO//xLSkp45ZVX8PPz45133lEbClJSUlq5FRQU\nFDB//nwSExMBmz3Thx9+yJEjRxg9ejRVVVUUFxczePBgGhsbaWpq4syZM7S0tDBw4ECqq6upqalR\nZxwpqU2lTk2j0aiNB3C+Zs3T01M9V3nd0KFDqa+vx9fXF29vbyorK3F3dyc8PJwhQ4Zw3XXXsXr1\naiIjI5k5c6b6yRbg8OHD6HQ61XJKr9erKc6AgABuu+02Hn/8caKjo5kxY4YIrm5CatQEBYvFQkVF\nBZ9//jm/+93vWg16veqqq1i2bBnTpk3r0vXtTdMTEhIcapquCLRhw4bh6+vrsOsKzos0EwjdTlvx\ncejQIaZPn87x48cZMmRIq9RfezZTimXTwIEDSUhIYOTIkfj6+qLX6/n2228BGDlyJD4+Ppw5c4ay\nsjJ1DIfRaGTQoEHqCA+tVktLSwuNjY3qery8vGhpacHd3R03Nze1E9R+1EdzczMWi4XZs2dz/Phx\njEYjoaGheHt7M3nyZPbv309mZiZRUVH88pe/5ODBg/j6+rJgwQIAdW7c3Llz1d8xJCSE77//nvnz\n5zN27Fg2btyIu7v7BdG0S4k3iaxdGhFqQn19PSaTqVUHZ1t/y7lz53ZJpCmm6Z6enjz//PMONU1X\nUpxKBE3oP4hQExxKZ30s58+fT3NzM5988olaSK+kBZTHylw1k8mkGrj//e9/p7a2lsmTJ1NRUUFo\naCi1tbWcPHkSsKUbiouLVeHl5eVFTU0N9fX1NDU1odVqW9WgKC3sDQ0NalRNGZTb0NCAh4cHnp6e\nNDY24uPjo5q4Z2Zm4uvry9ixYwHUzfPjjz/mvvvuY+TIkdxxxx1qN2tUVBSJiYkUFhaSkJCgHjMY\nDPz000/84Q9/4Oqrr+bFF1/klltu6fQ9FTqHCLX+icViwWw2YzQaaWhocHgHp4K9afqSJUu46667\nHJaKFIEmiFATeoWSkhKuv/56jh49isViwWAwqOM6lBlkShq0oqKCiIgITCYTLS0tvPjii9x///2E\nhoaSm5tLcXExPj4+5ObmEhYWxunTpykoKMDDwwM/Pz/OnDmDxWJh0KBBqm2Up6cnHh4e1NXVXbA2\nLy8vGhsb1RQDoA7FbW5uJigoCKPRyHXXXQfYio+nT59Obm4uzc3NHDx4kLCwMKKioggODlbFXHx8\nPKmpqQDExMSotlMpKSmMGTOGxYsXU1dXx5/+9CeuueYadT328+iEK0OEWv+isbGR8vJyysvLgfNd\n3Y6mqKiI9evXd4tpukajQavVotfrW7kICP0PEWpCj9F2Xthzzz1HeXk5H3/88QU/T01NJSYmBoPB\noHZNKqnQrVu3sn//fn7961/z4YcfMnnyZPbuPe9IpmzSSiq0trYWjUZDU1MTQUFBauSsrKyslSiz\nWq0MGjSIqqoqtVvUzc2N5uZmAgICMJvN6ntotVquuuoqzpw5ow7LvPnmm6mvr8dsNnPkyBFmzJjB\n3XffTXZ2NmPHjlVTLnFxcWrEUGk2CAkJYdeuXezcuZN//etf7Nu3j+rq6k5FJ4VLI0Kt72O1Wjl7\n9ixlZWWqy0h33avy8nI++OADdu7cySOPPMK8efMcJqZEoAltEaEm9DhKDZaXlxdTpkzhiSee4JFH\nHlF/bi9AlAhbeno6AQEBxMTEYLFYuPPOO2loaGDJkiW8/fbbXHfddWi1WjIzMxkwYIBq9+Lv768O\nv21qasLT05Oamhr1E7Zizq7YrCjNBW3x9vZWu0YHDhyo2lPdeuutNDQ0cPLkSXx8fIiPj8dsNrN/\n/35MJhOLFi0iPDy8VXNEYWEhAA8++CDjx49vNUPtxhtvZObMmdx111288MIL6v0SUdY1RKj1XZqb\nmyjL0rcAACAASURBVKmoqMBkMqlDrrsLe9P0GTNm8PTTTzN48GCHXFuj0TBgwAD0ej1ardYh1xT6\nBiLUhB7HXnhs2rSJ5cuX89xzz7F48WK10B4gKytLHcMBqDZTYEtFvvTSS5hMJiIjI7n66qtbNReM\nGTOGwsJCvv/+e3x8fCgoKMDPz4+6ujqsVitNTU14eHhgtVrVpgHl74WPj4866gNQGwu0Wq3aRaqc\n7+vrq/qGarVampqaiI6OJi0tjbKyMqZNm8Y111xDWFiYakGl/C5K/ZriEarcmzNnzjBjxgxOnjyJ\nyWS6oFHAvhlB6BxOKtTcgcPAKeDfgEBgKzAC+An4BVDZ5jWyf2H7t1dXV0dZWZka6e7O+9Lc3Exi\nYiLvvfceN954I0uWLHGYaboINOFSdGX/kjlqwhVhLzAeffRRpkyZwrRp06ivr+eRRx5RxUhsbCxw\nPgKXmppKRUWFKngmTpxIWlqaau1kMpnUsRxKOtLPz48TJ07g5+enCrLGxka1SUDx/7RHmcum0Nzc\nrDYc+Pr6Yjab1e7R5uZmvL29ue6669i/fz86nY709HT0ej1ubm7s3bsXNzc3dc5aZGSk2gH61FNP\n8cEHH7Bx40ZVfCm1ehMmTGD16tW88sorF6yvu+rVJHLX4yQARwG/c89fAb4G3gSWnXt+4V+AfkxL\nSwuVlZWYTCZ1NqKjse8E9fT05Prrr+frr792uGm6RqPB19eXoUOHdlmgXcqzVOi/ONun084in0g7\nSWf/43bEf/BffPEFixYt4j//8z959NFHW11XEWr2NV1ZWVkcPnwYq9VKSkoKp0+fZtasWeTn56vp\nTLCJrrKyMgoLCwkLCyM3N1cdaFlXV6c2CyifypXhuND6E7r9uA6lm1Rp6bdYLISFhVFWVsbYsWMp\nLy+nqamJmpoazGYzERERvPTSS7z55ps88MADpKenEx0dTXh4uBolVESp4n0aHBxMbGwsO3bs4JZb\nbunUPRah1TFOGFEbDvwV+B3wAraIWg4wDSgF9EAqENnmdf1y/2pvtEZ3sG/fPlatWtVqtpqnpycL\nFizg2WefdUgnpyLQ9Hq9amvXFS7mWSpirW8gXp9Ch3T2P31HiINJkybx9ddfs3TpUlatWtVKdCjf\nY2NjycrKUmes6XQ6Hn/8cZ555hlCQ0P57LPP8PX1JSYmhujoaKKjozl27BgAAwcOZPDgweqA3Nra\nWgICAvDw8FAH4ML56JmXlxc+Pj6qJZXSXAA2oaZYUHl5eeHm5kZFRQVarZacnBzq6uqoqKggODiY\nkJAQcnNzqaqqYtWqVRQXFxMUFMTEiRNVy6rg4GB1llxwcLDaNPHXv/6V2bNn88MPP1xwvxTxav9d\nRJpLsRp4GbAvqBqKTaRx7vvQnl6UM2GxWKiqqiIvL4/8/HwqKipalR50B5s3b24l0sDmfpKZmdll\nkaY0CYwaNYqrr77aISINOvYsXb9+vUOuL7g2PS3UZmD7xHkcW1qgI24CmoE5PbEo4fJpz7MyJCSE\na6+9luTkZFatWqUanJeUlLQ6X4k0paenq9ZL33//Pa+++ip33303X331Ffv372f79u0UFxfz6KOP\nMnnyZFpaWtQUqF6vVyNiVVVV1NfXq5uwxWLB3d0dq9VKfX29mtpUukIVA2Wr1YqbmxtVVVXAed9A\npTs0NDSU8vJyIiIiCA8P5/XXX2fDhg3k5uaqNXgBAQHq76V0thqNRvXnw4YNIyEhgRkzZlBfX3/B\nfbO35rKvYxOcnp8DZ4Dv6PhTsvXcV7+jsbERg8FATk4OxcXF1NfXd6s4UygtLSU3N7fDNV0pGo0G\nd3d3hg8frg7mdiQdeZa2LeEQ+ic9WaPmDrwNTAeKgUPAl8Cxds5bBezGudIcgh3tRX6UiFBwcDCf\nfvop8+bN45NPPiE4OFgtnFeiThkZGcTHx5OSkkJUVBT+/v5s2bKFMWPGMGnSJHbt2kVcXBxg890M\nCwtTZ7ONHj2a48ePYzabaWpqIjIykpMnTzJo0CAMBoM6nsNisah2Uw0NDa0sp5TOUOWclpYW3Nzc\ncHd3p7q6Gq1WS15eHiNGjOC7775j6tSpfP7555SVlREWFkZaWhoJCQlqp+eGDRv405/+pHa4JiYm\nEh0djV6vZ8aMGQQEBHDXXXfx+eeft7p3er3+siJpEnVzGiYD9wAzAR/AH/j/7d17WNRl2sDx7yBy\nPp+CQUZBJFxCC+kAS4puG7lbGVbrG7W52ttbu6Z02M01vXZrbWvd2tLMtXotrs0ky4rKSHH3NWxN\ny5RySURFzAMwihyEOMrh/ePH7+cwAoIOc4D7c11dDsPAPAzNcM/9PPd9r+XclqcRCEMJ5s7z5JNP\napdTU1NJTU0d1MVagzpX9/Tp01rBj7XU19fzxhtvsGHDhl4byl7s/E+dTkdAQAAhISHamzxL621m\nqaUDQmE9+fn5Ws/NS2XNQCgJ+CNKVg3OHbD9i9ntHgZaUbJqnwDv9/C9huUZD3tjHjSYj0H6/vvv\nue2223juueeYPXu21vRVDWZM21pUVlaydetWMjMzycrK4l//+hd79+7l6aef5oMPPiAmJobw8HDq\n6uowGo2UlpYCUFZWRn19PS0tLTQ1NeHn58cPP/zAiBEjaGlpoa2tDScnJzo6Orqde4NzZ9acnJwI\nCAjQArSGhgYCAwO1yQjjxo2jpaWFUaNG8emnnzJx4kQMBgNRUVH4+PgAUFdXh8Fg0IKznqY0ZGVl\nsXbtWlavXs3UqVP7fCzF+ezwjJpqCvBblDNqfwWqUN5s/h7w4/xigiHz+qVmraurq7XM9GC21jDX\n2trK+vXref3117n++ut56KGHOHDgwHln1C5m/qc6TWDUqFG9BlKWImfUhj5Hac9xB5AG3N/18T3A\ntcB8k9uEA28B04A3gI3ABz18ryHzQudoBnogPicnh0cffZSCgoJuQZIanKljmQBtckFsbCybNm1i\n06ZN7N27l9dee40PPvgAo9GoNcb18fFh//79eHp6MnLkSAICAigtLaWiooKQkBDq6uoICgqisrKS\n5uZmbSJBR0eHdlats7MTFxcXnJ2dtcpRT09PAgICqKys5PLLL9eCrOrqamJiYmhtbWXHjh3cc889\njBs3Dj8/P/z9/bVKULXXGtBtxFRlZSVBQUEsX76ckpIS3nzzTTw9PbVCi8LCQq0Yoa/HejgHdHYe\nqD2GkmELAN4FDAzh9hxq37Pq6mra2trOy55Zev6mOdOh6VFRUTz88MPExMRY5P7VzLter8fHx8di\nY6QuJDc3l5UrV9Lc3Iybmxvz58+XIG0IcZRA7XaUbFpfgdoG4HngK5Rqqo1IRs3hmA8kX7BgAd99\n9x3/93//R0VFRbfbqudY1AkGxcXFZGRk8Oc//xk/Pz+KiorYsGEDEyZMYNKkSZSWltLU1IS7uzs7\nduwgKipKmwN45swZLXvW1taGh4cHTU1NWnZNbXbbE3VeqLe3N2fOnMHLy4vGxkb8/Pzw8fHh9OnT\nJCcnA/Dll1/S1tbGL37xC8rLy4mLi2PatGlUVVWRmpqqFUoAWgZRrXStqKjg+eefp6qqildffRVX\nV9d+DWsfzgGayo4DtYFyyNcvdWuzqqqqz6kBPVVdXkxGqzeDPTR9sLc5xfDkKIHadcCTnNv6XIRS\nLbXM5DalJmsKAhpRAruPzb5X5x//+Eftg6FyxmOoMA/UWlpaSE5OZvbs2SxYsICCggItm6ZmrPLz\n87UGsmqvtfT0dAoLC3nmmWcoKSnh1ltv5dChQ8C5sxu7d+/miiuuoLS0lLa2Ntrb22ltbaW2tpa2\ntjbc3Ny0d6hqZk3tfD5ixAitQlTV0dGhBXOdnZ24ubkxYsQIQkJCALjzzjspLS1l8+bNeHp6MnPm\nTMLDw7XMmtqqQ80MVlZWkpaWpgVaeXl5/OQnP+HGG28kICCAd999Fycnp15ngQ7nAM38jMdTTz0F\nEqhZXVNT04C2Nh944AF27Nhx3vXJycm8+uqrF72Offv2sXz58kEdmm6NbU4xPDlKoOYMHAB+ApQD\nu4C7OL+YQJWFbH0OGYcPH+b6669nyZIl/OY3v9GKChISEro1ijUN2tSs1KZNm/jiiy/4/PPPSU9P\np7m5GQ8PDzw9PTl48CBubm4UFRVRX1+Pv78/dXV1uLi4cOrUKSZMmEBBQYHWouPs2bO4urp2y6y1\nt7dr2x1OTk40Nzfj7OyMp6cnbW1teHl54eHhoRUvJCYm0tbWxo4dO4iNjeWBBx5g165dZGRkaAPo\n1e1QQAtKTbc5U1NTmTx5MjNnzmThwr4KoIVKMmrW09bWpjWl7Wlrsy9z5szRKr5NJSYmkpWVNeC1\nDPbQdFtsc4rhx1EmE7QBDwF5KJWdr6MEaQ90ff7i32oJu2NeWDB27Fi++OILpk6dSnV1NYsXL9Ze\nFNVgDdAGuRcWFlJcXExgYCB1dXXEx8czatQo3nrrLRITE/Hx8aGxsZHw8HBycnK45ppr8Pf359Ch\nQ5w4cQJPT09iY2O13kl+fn60trZSU1ODk5MTzs7OWrPcjo4OrVWHTqfTJiC0tbXh7OxMe3s77u7u\n1NfX4+PjQ0tLC1FRUXR2dlJVVcX69euJj49n9+7dREZGEh0drf2hUs+s5efnExsbS0JCAkajkX37\n9vHYY48xb948IiIitPFT6uOlslQ2bThn5kT/9Hdr80J6q64caNWl+dD0J5980qIDznU6HYGBgYSE\nhODkJC1Fhf1y1LcPdv+OVPSsoqKCadOm8bOf/YyMjAzCwsLOO4OVnZ2tbYOq24XqvNDa2loWLVpE\nQkIC48eP14ajnzlzBldXV0pLS3F2dsbPz4/i4mJaWlq47LLLOH36tDb/Uz2vdtlll2m9z+BcE1x3\nd3ftjFtAQIDWSV2dC9jY2IjBYKCqqorCwkJ+8pOf0N7eTkxMDCkpKRw5cgQ/Pz8ArQpUnQeampra\nbdbnH//4R6qqqvjgg54Sx8KUZNQGx0C3Ni/kUs+oNTY2snbtWtauXcv06dMtOjQdzjWtDQ8Pl21O\nYTUymUAMCks1XjXtvB8WFsb777/Ptm3bWLVqFSEhIeTl5WnBWnl5OampqQQHB2M0GikvL9cGnsfG\nxlJTU8Ozzz5LcXExO3fupK2tjaSkJOLj4wkPD+f666/HYDDQ0NDAPffcwzXXXIObmxuRkZHabM8R\nI0ag0+m07Jqvr692Vs3d3V1759/Q0KBNQujo6KCxsZG6ujr8/Pxwc3Ojs7OT0NBQSktLSU9P5+DB\ngxw5coTExESOHTtGdHR0t0BQzZqp59H0ej1z586lqKhIC9RMH/PeLg/W70kMH21tbZw+fZoDBw5Q\nWlpKTU2NdnbzUk2ZMoWFCxeSnJxMYmIiycnJ/QrS2tra2LBhA7fccguHDh1i3bp1LF682GJBmtq0\nNiIigsjISAnShMNw1HendvWOVAxcQ0MDM2fOxMnJiZycHK04wLTQoLCwEEA7qwbKea/du3cTHx/P\nkiVL+OGHH5g+fTpeXl7aGTej0ahtPR49epSQkBBqa2vp6OjAzc2NxsZGmpqauO666/j6669xdnbG\nycmJhoYGbSvUYDBgNBrp6OjAxcWFuLg4jh49SkBAAEFBQRQUFBAdHU1bWxsHDhwgISGB5ORkjEYj\nmZmZFBcXk5OTQ2pqKunp6VqLDrXIANDW2tDQwC9+8Qu2bt3K+PHjzyvGEArJqF0aS21tDkR/2mR0\ndnaydetWli9fTnBwMI8++qjFhqarZJtT2JqjFBNYkgRqDqKnaka1yW1cXBy//OUvqa6uJicnB29v\n7249xcwLDgCKi4vZvn27tsW4c+dO8vLyuPnmm7nzzjvJzs6mubmZSZMmYTQa2b9/P6dPnyYoKIiG\nhgaampqora0lLCyMo0ePau082tvbCQ4O5uTJk1pmzdvbm+rqam1uqKenJw0NDfj5+eHp6cno0aMx\nGo1888033HLLLVxxxRVERkaSk5NDenq61ltt+/btzJgxA6DbQHr1sl6v58EHH6ShoYFHHnlEe7zy\n8vLO663WX301I3ZUEqhd1B3ZrCFtf7ZAv/nmG1544QXt//2UlBSLHuiXbU5hLyRQEw7BvMBAr9dz\n/PhxFi5cyOHDh3n99ddpbW3tVgkKaH3JTCcZbNq0icjISO17/elPf+pWKRoSEsKRI0fw9PRk/Pjx\n7N+/n5KSEry8vAgICMBoNOLi4oK3tzenTp2b8uPu7s7Jkyfx8fGhvr4eNzc3PD09GTFiBNXV1ej1\neq3QAGDChAns27eP6upqrr76aubOnUt2djYGg4ElS5awaNEiQkNDmTVrFpWVlZSUlJCUlKT1jlPV\n1dUxefJkXnnlFWbOlBG3PZFArf/UFjU1NTUDrtq0lL7adDz++OMsX76cAwcO8NBDD/Hzn//con3L\nPv/8c9atW4dOp8PT05MFCxZI81hhU3JGTTgE04yOejkiIoJ169YxZcoUbr/9du3zalbJaDSSlpam\nnfUqLCwkNDSUyMhIAgMDqampwd3dnbfffpulS5dSXFxMSUkJl19+OSkpKYSEhLBz505cXV0JCgrS\ntj4DAwNxdnamtrZWa9XR0tKCs7Mz7u7uVFVV4e3tjY+PD66urtTW1nLdddcxcuRIoqKicHZ2JjQ0\nlFOnTnHddddRV1fH5ZdfzhtvvKENUs7KysLT0xMfHx8qKyvJzs7WhrgHBgZSWFioPQ4+Pj68+uqr\nPP744zQ3N1NQUKBtgarZRFNyLk2Ya29vp7q6mpKSEg4dOkRlZSVnz561SZAGvQ9BP3jwIHPmzGHS\npEls3LiRW2+91eJB2nPPPceOHTv44osv2LJlC5mZmeTm5lrsPoSwJgnUhM1VVFTw8MMPc8cdd3DH\nHXewY8eO8wIRdZtQzZip2ajo6GiSkpK46qqrcHJy4t133+XHP/4x69ev58033+T06dOEhYXR0tKC\nn58ffn5+1NXVMXLkSG666SZaW1sJCwsjJCRE2+pUG1/6+/vT3t5OUFAQ3t7etLS0cPbsWb777jsm\nTZoEwLFjx6ivrycmJobc3FzCw8M5ffo03t7eREZGaluegLaNWVlZSXBwMGlpaeTl5WE0GiksLOTa\na69l0qRJ3HfffUycOBE4PyBTCy4cfRtTWEZHRwd1dXUcOXKE4uJiKioqaG5uprOz02YBmqqvNh0b\nN27kV7/6lUW3I9XsWU5ODt9//323zx0+fJiVK1da7L6EsCYJ1ITN6fV69Ho9t99+O7///e+5/fbb\nef/999Hr9dp2p16vJzs7m8rKyvM61qsH9/Py8tizZw8RERE899xzpKSkUFJSwpdffsmpU6fw9vYm\nJCREa7Px0Ucf4e3tTUVFBWFhYSQnJ+Pp6Ul7e7sWzLW3tzN+/HiampooKyvjxIkTzJ49m71799La\n2sr1119PUVERUVFRlJWVATBq1Cjq6+sBpdWIqqamBoCSkhIqKytZtWoVaWlphIaGkpaWhl6v55ln\nnqG8vJx7772XsLAwAO0xMH2sxPDV2dlJQ0MDx48fZ//+/Zw4cYKGhga7CM5MZWRkMGrUqG7XhYWF\n8cQTT+Dr62ux+zGv5jx79myPt1Mz3UI4Gkc97yFn1KzM0lmcvr5ffn4+d999NykpKWRmZjJmzBit\n95h54Kb2JVMvq+fXAG2s0+HDh3nzzTc5evQofn5+XHnllfj6+mI0GqmuriYgIABfX18MBgPbtm3D\n09MTo9FIXV0dnp6eNDU14eLiwhVXXEFFRYWWQWtpaaG6upqmpiaioqL497//zeTJk7UealdeeSV+\nfn5aLzXTMVmmA9vhXJYtISGBgwcPMnv2bK644gpee+01dDpdr4/XcBrcPtzPqDU3N1NTU0NtbS2d\nnZ1WKwq4GB0dHeTm5vK3v/2Njo4O9Ho9vr6+Fh/OrtPp8Pf3JzQ0VKvmTEtLY8uWLefdNi0tjc2b\nN1vsvoUYCCkmEENObW0tDz74IPv372fVqlVERUVpQ9vVDv+mWabs7GwtYwVKo9lNmzZRV1cHKM1q\nP/74Y/7zn/9w6tQpkpOTCQ0NpaioiMTERKqqqigqKsLd3Z2KigqCgoJoa2ujvr6eyMhIjhw5gr+/\nv9YZvaysDH9/fy677DJ8fX3R6XR89tlnhIeHc91112mTEvbu3atl12bMmKG1DVm8eHG3Cte8vDxt\nW3fnzp1MnTqVadOm8cILL2jBaE+VnOrP31+OHMQNx0Dt7Nmz1NbWUl1dbbOigIFSh6a7uLjw8MMP\nW3RoukrNohkMhvOmFeTm5pKZmcnhw4e168aOHcuKFSukoEDYjARqwu5dTIDQ2dnJK6+8wh/+8Ad+\n+9vf8tOf/rRb5SdwXoWouiWqDkQvKSnRAiYfHx8SExN5//33efvtt+no6CAmJoba2lp8fX0JCgqi\nrq6O2tpaDAYDBw8exNvbG09PT1xdXamurqa2tpbx48drfd8MBgNZWVm0tLRwxx13aOfZ9uzZw6RJ\nk9izZw/p6emAEnyqQZ+adfP399dGZqkZNVAKCF566SW8vb1ZtGgRIH3Vhkugpm69V1dXa9t1jvB6\nN5hD0031lEUzl5uby8qVK2lubsbNzY358+dLkCZsSgI1MSSowZwaiIWGhqLX69mzZw933nknqamp\nPPDAA0RERABo26Fqg1yV6XYiQFVVlTZzc8WKFQDceeed3HHHHdTW1tLc3IzBYCAwMJB77rmHFStW\n4OHhwcSJE9m9eze/+c1vOHbsGKtXr2by5MlaO4+GhgbOnDlDdXU1kyZNIjk5mX379uHu7k5wcDDe\n3t6Ulpbi4eHBNddco80ATUxMJDg4mJ07d5KUlKStU82oqY1wi4qKWLhwIR9//LF2Xq2nbc6err/Q\nY+yIhnKgpjajra6upqGhAZ1OZ9dbm6YGc2i6KdOzaJ6enhb93rm5ubz00ku0tLTg6uoq7TyExUmg\nJuzehQKEvs5ggdLf7LbbbqOuro4PP/yQ4uJiLQNVUFBAcXExGRkZ5OXlAUrQYzq+aevWrUycOJHY\n2FjtDNvmzZv5r//6LzZu3MjXX3/NDz/8QFhYGAaDAR8fH86cOUNpaSmurq5MmjSJpqYmioqKCA8P\nJyIigs8//5zOzk4SEhI4fvw4EydOpKysjJaWFgBcXV21bJrK399fO2eUmJjI1q1bWbZsWbcgNT8/\nnyNHjvCrX/2Ka6+9lk2bNnULRE0fL0cOvAZqqAVqnZ2d2pxNdYveUYIzOH9o+uzZsy06NN2UTqfD\nz8+PsLAwi08WkK1SYQ0SqIlhoaysjNWrV/PKK6/w4osv8stf/hLoOROnZtVU6tk2NUj77LPPSE9P\nZ9++fQCEh4ezceNGjEYjR48exc3NjfHjx+Ps7MzUqVPJyckhJiaGgwcPEhgYyIEDB3B2dmbSpEl4\neXnR1NREXFwcAKWlpTQ1NZGRkUFNTQ379u0jPDycuro6re0GoG15bt26lczMTO28munP8cILL9DR\n0cE999xz3oQH8+KKoR60DaVAraKigpqaGrsvCuhJY2Mjb731FmvXruWmm26y+NB0UzqdDicnJyIi\nIvDy8hqU+5DiA2ENEqiJIc08ANm+fTt33XUXN9xwA0899RTOzs7a54xGY7dCA9XTTz9NSkqKNr1g\n586dREdHEx8fT1ZWFqBMB9izZw+XX345GzZs4PTp01qxwLXXXktjYyPHjh1jz549+Pj44Ofnh4+P\nD2lpadoW5969e0lOTiY8PJyysjLt34aGBq2PWl5enjYPNDAwUDtHp84ABbQzd1u2bOGZZ57h4MGD\nvT4ew8VQCtTUObaOpK2tjZycHF555RWuuuoqFixYoLW6GQw6nQ5fX1/CwsIs2hDXXGpqKtu2bTvv\n+ilTpnRrAyTEpZBATQxZvQUlp06d4u677+aHH37gqaee4oorrui1TYVphkptkQHK9uimTZu0QCom\nJobIyEjy8vJobGyksrISLy8vduzYwciRIwkLC+PgwYPMmDFD21YNDw8nJiaGsrIybf4oKP3TMjIy\nKCsr01pvNDQ0kJGRAShbsWqwN2/ePAoKCti5c6e2VaoGnCdOnCAhIYH8/Hx+9KMfXfBxGcokULMN\n06HpISEhPPLIIxYfmm7KGlk0U5JRE9YgI6TEkNRXMNLW1sbmzZtJTk5mzpw57Nu3T8uiqefU1GID\nvV6vBVYZGRlUVVVRVVUFwJw5c/D29gYgMjKS7du3A0qgdO211xIXF8cjjzyCm5sbTU1NzJw5E4PB\ngJubGy0tLVRVVWmBXk5ODp999hmbN29mypQpREZGEhcXh4eHBw0NDTQ2NrJ7927WrFnDtGnTAKWN\niFq1mpSURGFhodaGpLy8HCcnJ5KTk8nKytKmEvQ0UkqIwfDNN99w7733smrVKh5//HHWrFkz6EGa\nj48PMTExVgnSABYsWMDYsWO7XTd27Fjmz59vlfsX4kIc9d2pZNSGOdMgbv369SxatIirr76a3/3u\nd4SHh3c7s5WXl6f1KktLS9OmBaSmppKTk6O1zdi7dy/Tpk3jo48+IiUlBYDVq1fj6+tLc3Mz/v7+\nHD16FKPRyM0336ytJS4ujn379lFYWKgVHvj4+PDRRx8xe/Zsdu3axTXXXEN6ejorVqzQzqkdOXKE\nxMRESkpKSE9PR82yqIUQahVoQ0MDDz30EJs2bepWDWs+5B76rv509CycZNSsp7S0lBdffHHQhqab\nU7Noo0aN0t44WZO08xCDTbY+xbBjGpiUl5fj7+/PsmXLWLlyJbNmzeKmm24iMTFRy6qB0q6jqqqK\njIwMbTtUva6mpkaryFSb5aojodRzZikpKaxevZrQ0FCt5cauXbsA2L9/P6NHj8bDw4P9+/cze/Zs\n8vPz+e///m8tMIyJiQFg+vTpWnGDelYuODiY0NBQCgsL2b17N3PmzNEKIiZOnMioUaPYsGGDFkD2\n9Hg4chDWHxKoDb6TJ0+yevVqtm7dyty5c7nrrrssOo+zJ2oWTa/XD2owKIQtSaAmhpWeOvSrnweS\nCgAAGuxJREFUAdvRo0dZtmwZ3377LS+//LJWKWmaeSosLKSqqkobOWUarAHs2rWr28H/qqoq5s+f\nr00VOHjwIJ6ent0KBgAtK1daWgqgBWlpaWnk5ORovdUyMzPJysrCz89Py6SZtt9Q16r2iAsODual\nl17qNgtUvZ1p0YQEag7D7gK1+vp63njjDTZs2MDMmTO57777zpvHuW3bNrKzs2ltbcXFxeWSx0HZ\nOosmhDVdyuuX84VvIoR96W27T/33ww8/ZPPmzcyfP5/k5GTWrFkDoJ0FU2dt6vV6rbhA7cEWHBys\nZdbS09O7VYkuXryYhQsXauvw8/OjrKxMmzZQU1PDxIkTKS0tJT09nZKSEjIyMigpKSE1NZVjx45h\nMBi0SjJ/f3/y8/OJjY3VgjX1cxkZGYSGhmrbnBMmTGDdunU89NBD2s+q/jymj0dvwdpwyLiJgWtt\nbeWdd95hzZo1TJ48mffee0+rODa1bds2li1bxvHjx7Xr1MsXE6zpdDq8vb0JDw+XLJoQFyDFBMKh\nmGeQzIMP9eObbrqJjRs3cuLECZKTk6mqquoW1Khn1lJTUwkODqa8vJySkhKt6EDNdFVVVbFz505A\nya7NmjWL0NBQvL29tR5sOTk5+Pn5sWvXLo4cOaJNP9i3bx9PP/00/v7+WpDm7+9PYGAg3377LYGB\ngdr2p7r22NhYUlNTte1S9YxdVFSU1qtK/RkSEhK6/fym27xC9KWjo4NPPvmEW2+9la+++oo1a9aw\ndOnSHoM0UKqYTYM0UAI19f/TgVArOg0GgwRpQvSDZNSEQxlIVig2Npa//OUvbNiwgYSEBD799FMt\nuCsoKCA4OFj7fkajkfT0dG3Ae1ZWFnPmzNG2KP39/bVKUR8fHyIjI7U2HyUlJSQlJWlFCWqgFhcX\nR1xcHG+88QZz586lpqZGmzm6aNEiiouL2bp1K9OmTaOqqkrb6gwNDdV6qqnr/Pe//01ISAhGo/G8\nQgLTzFpvf2h7a10ihh91aPrIkSNZunRpv4amt7a2Duj6nuh0Ory8vAgPD+/W+1AI0TfJqAmHYN7A\ntr+uvvpq/vrXv/Loo48yefJk/vGPfwBKQ1nTAe/qNIM///nPxMbGsnjxYgoLC5k+fTrp6els375d\na04LUFNTw+7du6mqqiI6OloLkPbu3dtt+sCxY8eYNGkSNTU1REdH4+Pjw5w5c1izZg2xsbFkZmZq\n5+PUzBoohQ9q4BUaGoqzszM1NTXdJhGoTCcW9Df4kiBt+CkqKuL+++/nmWee4f7772fdunX9CtIA\nXFxcBnS9OfUs2ujRoyVIE2KAJFATDqGvOaD9kZmZSW5uLk888QRLlizRhpyDEhSpDWYjIyNJSEgg\nLy9PO+BvNBpJSUkhPj5em9GZnp7OnDlzSE1NpaSkhJycHMrKypg1axZHjhxh2bJl1NbWanNDVZGR\nkYCSbXvnnXcACAwMJCkpqdvPGhwcrG1j6vV69u/f323rU/3Z1d5qAw28LjbwFY7nxIkTLFy4kHnz\n5nHDDTeQk5PDjTfeqB5u7peMjAwiIiK6XRcREaE1cO6NmkWLiYk5rzhBCNE/jlpBJVWf4jz96SV2\n4sQJpk+fzlVXXcXLL7+Mj4/Peefe1ErPjIyMbme+du7cSVJSktZGQ6VufRYXF7N9+3ZmzJihVXuq\nxQiAVsG5adMmEhMTAbTPmepp+/LZZ5/Fw8ODzMxM7TrznmqmP/tQnP8pVZ8DU1NTw2uvvcbGjRst\nMjR9oFWfTk5OhIeHS4AmBNKeQ4g+mQcrhw8fZu7cuezZs4epU6fy+OOPk5KSwjfffHNe4GNKzbpl\nZ2drzXL9/f21Nh+m1qxZow1iV8+gAVqfNlACsqysLBITE9m9e3e3cVJwru9bbGwsK1euxN3dnSVL\nlgCcF5wNh4pPCdT6x5pD03ui0+nw9PRk1KhRss0pRBcZISWGNdOgqqcAy/TQfXl5OWPHjmXbtm18\n8cUXXHnllfzP//wPsbGxvP/++5w6darb1xQWFmqtPNTvUVNTg9FoJCkpiZqaGi27VlxcTGVlJQkJ\nCcTFxZGYmIjBYGD37t2kpqZqQdrOnTu1rNycOXMIDg5m+vTpJCUlaeOvQMm2paamkpCQwA8//EBI\nSEivAZd5X7nePieGrra2Nt577z1uueUWDh48yFtvvcXixYutHqTp9Xo5iyaEBckzSTgc8wxRb5dN\nb1teXt7t0H15eTkTJ05k4sSJ/OlPf+Ljjz9m/fr1TJkyhalTp3Lfffcxffr0bluTaratuLgYUDJe\nSUlJVFZWUlxcTGpqqlZRqmbN1IkDan+00NBQ5s2bx6pVq0hKStKuB2WklXof6pD2pKQkjEYj7e3t\ntLW1dRuLFR8fr922pyKD3h4vMbSoQ9NXrFhBUFAQK1asGNR5nD3R6XS4urpiMBj6XWAghOgfyagJ\nh3MxQUdv/dZA+SNz9dVX8/bbb3PixAmuv/56nn32WQwGAytXrqSxsVG7bUFBgRZQpaWlUVlZSXx8\nPBkZGd22P02DOaPRSGpqarfvER0dDSiFBHv37gWUrdXCwkItqJw3b55WnXrixAmmTJmiBZ3q5ATT\nAFS9f/Nig76ybcKxmQ5N/93vfsfrr79ukyAtKCiIsWPHSpAmxCCQjJqwKmtndwZ6X97e3jz22GNM\nnTqVuro6PvnkE2677Tbi4uK49957aWlp4cYbb+Sdd95h8eLFxMfHdwvQ1MHvgNY8V82MqcHZmjVr\nmDFjhlY0MG3aNG0Qu1ppqk5JACUAO3PmzHljdtSATA2+QkNDtce3t3NrklkbGkpLS1m+fDnFxcVW\nGZreE51Ox4gRIzAYDJdUpCCE6Jtk1IRVWTtQMG9j0dttTKsly8vLCQ0NJTU1lUcffZTy8nIyMzP5\n6KOPeOmll5gwYQJvv/02W7Zs0QoM1H/j4+O7nTMDqK2t1So+Af7+979rl9VsmBqkqesoKSnReqi1\nt7dz8uRJTp48qa21oKCgW/sO03N0qv481uaPiWTc7NupU6d48sknufvuuyktLSUsLIzc3Fy2b99u\n1XWog9THjRsnQZoQg8xRK6ik6lNYRG9tLEyvh+5Bz4kTJ9izZw+//e1vMRgM/OEPf2DcuHEUFhYS\nHBysBV9qViwhIUE7R2Z6ngzQhsKrZ9lMPwal8/tdd93FnDlzuPnmmwG6fb26RjVQHMqGc9VnfX09\nWVlZvPvuu1x99dXs37+fsrIy7fMREREsXLjwkoak95e03RBi4KTqU4iLZD7QXWV63gu6Z+TUWYX/\n/Oc/SUlJIT09nUceeYTExERCQ0MpKCjo1jBXzdCVl5dTXFzcLSjcuXOntu0JSmZNPft2/Phxbrvt\nNu6//35uvvlm7byaui7TNZoGaWp1a1/ZMcmcXbII4DNgH/AdsKDr+gDgn8BBYAvgdyl30traytq1\na7n55puprKzkvffeo7GxsVuQBhc/d3MgdDod7u7ujBs3ToI0IaxIAjUhTKgBjHnWSg2MTD8/ZswY\nnnrqKd577z2Cg4OJjY3ltddeIyAggLS0NAoLC7UqTvU/taigvLyc/Px85s2bp22Zmq6hsLCQefPm\nsXTpUp544gktkDNlnkEzXZu67t5+PnHJzgKPAHHAdcA8YDzwe5RALQb4v66PB8x0aPqXX37ZbWi6\nJeZuDpROpyMkJISoqChGjhw5aPcjhDifBGpiyOtPcNLTFqdpNk3dslSzWKbfMzY2lpdffplt27bx\n1VdfMW3aNF544QVuvPFG7bamW51qdac6eF0N2vR6PWlpaWzcuJEXX3yRxx57jPvvvx+gWyBnOi3B\nlGmvN9O193QbCeIumRH4tuvyD8B+IBy4FfhH1/X/AG4b6DfesWMHs2bNIjs7m6VLl7Jq1SrGjRun\nff5S524OhE6nY+TIkURFRREcHDygsVNCCMtw1GednFETdqGn0U3/+c9/eOyxxwgNDWXy5Mk4OTmR\nmJiITqfDyckJnU7HoUOHcHJy4vLLL+fQoUOcOXOG6Ohovv/+e/7617/y/PPPM3XqVACtoa5pSw71\nPns7Y2feW828YOJiizps2ZPNjs+ojQG2AVcAxwD/rut1QLXJx6oez6gVFRXx4osvUlFRwYIFC/jp\nT3/aY2C0bds2li1bxvHjx7XrBuOMmk6nw8/Pj7CwMJyc5D29EJdCRkgJ0QNrBBVqQGR6n0ajkaCg\nID799FM++eQT2tvbaWpqwtXVlaamJlxcXDhz5gwuLi64uLho13V2dlJfX8+SJUuIiorS2neYj7Tq\n6WNrsPWYKjsN1LxQgrSlwIdADd0Ds2qUc2umOn/9619rH4wZM4b8/Hy+/vprHnzwQWbOnHnB7cWB\nzt0cKPUcpnlLGCFE/+Tn53draP7UU0+BAwVqNwHLgRHAGmCZ2efvBh5HWVs98GvgP2a3kUBNDLqe\ngo/eBr+bZ6xMb2P6sdq6Q93K7E82zLRiVA3ezKs8ze/TPIDs7ee50M9lT+wwUBsJfAJsQnlNAygG\nUlG2RsNQCg5izb6us7CwkOrqav73f//XYkPTLUGn0+Hh4UFERISMgBLCghyp6nME8DJKsPYj4C6U\nA7imSoHJwASUd6mvWXOBQqh6ClrUooCBfK3p5fj4eK1Jrnq9aZGCWiGqnkPLzs7WgjbTM3JqwGZ+\nH+YFBabX9XUuzfznkvNqF6QDXgeKOBekAXwMzO66PBsly3ae1157jRkzZtDW1saHH37Ir3/9a7sI\n0kJDQxkzZoxVg7Tc3FzS0tJITU0lLS2N3Nxcq923EI7A2m+ZrgFKgO+7Pl4PzEA5iKvaaXL5K2CU\nVVYmhr3+bN+Zn/kynQTQ023VzJd54GYaWKmBWHZ2tjYvVA3I1CrR3ooc+jPntKf+cKZf01sPOdGn\nHwP3oGT7v+m6bhHwF+Bd4D6U17lf9PTF6tD00aNHD/5KL0AtGBg9ejSurq5Wve/c3FwyMzM5fPiw\ndp16+ec//7lV1yKEvbJ2Ri0cOG7y8Ymu63pzH/DpoK5IOBxLZXt6q4jsi3nVZF9boHq9/rzMl/lt\nTXuhqVWgQLctTtN1mrYNMf0+vT0mphWiPU1g6OtnFH3ajvL6eSVwVdd/m1HOpN2A0p7jRqC2py9+\n/vnn7SZICwgIIDo62upBGsBLL73ULUgDJVBbuXKl1dcihL2ydkZtIAfLpgJzUd65nufJJ5/ULqem\npnYbei2GNksFEpf6fXqqpDT9nuZNb9X7VM+Pmd+/eg5NvZ3p3FDTc2um26bqbU1biJhSA76+MoD2\nGpiZH8YVlqNWIEdERODl5WWzdbS0tPR4fXNzs5VXIoT9svbB3OuAJ1HOqIGyVdDB+QUFE4APum5X\n0sP3kWICYfd6CuT60yajv2fKevse5kUIva0Jei466O/PZG12WExwsQY8QsqSdDodXl5ejBo1yuqD\n3M2lpaWxZcuWHq/fvHmzDVYkxOBwpGKC3cA4lL5DLsAslMO3pgwoQdo99BykCWE3+ruFaB6kmTet\n7W9TXjWbpo6p6mvrVQ3ATNfYUxZvIOw1+yb6R6fTodfrMRgMNg/SABYsWMDYsWO7XTd27Fjmz59v\noxUJYX+svfXZBjwE5KFUgL6OUkjwQNfnXwX+gNKHaHXXdWdRihCEsCt9ZbP6ypyplZ29BT39ud50\n7ueFBsv3FcyJ4UGn0+Hq6orBYBiUCQYXSy0YWLlyJc3Nzbi5uTF//nwpJBDChKNuI8jWp7A7A6ka\nvdDXDHRL8kJfZ6nJBLYkW58XR6fTERQUREhIiIyAEsJGZDKBEFZirSDnQg1o+2qqa347S00TsOTP\nfjHfSwK1gVELBkaPHm3zHm1CDHcSqAnh4Hqa39nXbfubHetvQOQIWTYJ1PrPngoGhBCOVUwghMPq\n7cB/fwsBeru9+VmyC2XRTKl92Hq7TU8Ztp6+T18VpsKx2FvBgBDi0jjqu1PJqAmH0dfMUNWFtix7\nKxhQ9TQcvj9n4S4lk2btLJxk1PpmywkDQoi+SUZNCDtyoUyUaQattxmbalCmMv/YXG+zP3v7+EL6\nk02z963S4USn0+Hv72+zCQNCiMHjqO9OJaMmhoy+2nxc6vcaCtWeKsmo9UydMODt7W2x7ymEsCzJ\nqAlhRRdzdmsg59h6CrYu9ryYI4yKEhdHp9Ph4eFBTEyMBGlCDGESqAkxQJcS8PR2kN98mPvF3p/p\nFumlBHjCvul0OkJCQoiMjMTZ2dp9y4UQ1uSo2wiy9SmGpIttdGupNh2W+rrBIFufymMwYsQIRo8e\njbu7u4WXJYQYLNJHTQg7Yk/BjSl7XVd/DfdATafT4ePjg16vl7YbQjgYOaMmhB0ZjArLS/n6C005\nsOR9icGh9kaLiIiQIE2IYcZR351KRk0MS0Np0sBADceMmk6nw8XFhdGjR9vVMHUhxMBIRk2IYeJC\njXN7u64nPU1IsDbJ0PVOp9MREBBAdHS0BGlCDGOO+u5UMmrCoV1qxmsgX2+J7Jo9ZOiGU0ZtxIgR\nRERE4OXlZaUlCSEGk2TUhHAwlxr0mDax7c1AzqZdKLNl6yBtuNDpdHh6ejJu3DgJ0oQQgARqQliV\npbf6+gqgBhKgSSBmezqdjssuu4wxY8ZIbzQhhEYCNSGsaCDblRdjoF9nrQBNzqL1Th2mHhUVRVBQ\nkLpFIoQQgOOe95AzakJYma2zb0PxjJpOp8PX1xe9Xo+Tk7xvFmKoupTXL8mvCzFMXGpBgGyPWpaT\nkxPh4eH4+vraeilCCDsmb+GEGCb609rjQmQL0zLc3NyIjo6WIE0IcUGOuo0gW59C2IitWnUMpa3P\njo4OOYsmxDAisz6FEEPeUArU5PVLiOFF+qgJIYQQQgxBEqgJMUzJeTMhhLB/EqgJMQzZw0goIYQQ\nF+ao5z3kjIcQw4ycURNCOCo5oyaEsCjZFhVCCPvgqO9O5R2pEMOMZNSEEI5KMmpCiEEhmTUhhLAt\nCdSEEL2yVcGBBIhCCKGQQE0IYXccvCL1JqAYOAQstPFahBAObsgFavn5+bZewkVz5LWDY6/fkdcO\njr1+R157D0YAL6MEaz8C7gLG23RF/WBvvwNZT99kPRdmj2u6WBKo2RFHXjs49vodee3g2Os3X7uD\nb3teA5QA3wNngfXADFsuqD/s7f8fWU/fZD0XZo9rulhDLlATQjg2B9/2DAeOm3x8ous6IYS4KBKo\nCSEszsGzYpdC+m4IISzKUXsS5QNTbL0IIYRVbQNSbb2IC7gOeBLljBrAIqADWGZymxJgrHWXJYSw\nscNAtK0XIYQQw50zygvyGMAF+BYHKCYQQgghhBgupgMHUDJni2y8FiGEEEIIIYQQom+O1mTyDeAk\nUGhyXQDwT+AgsAXws8G6+iMC+AzYB3wHLOi63hHW7wZ8hbIlVQQ823W9I6zd1AjgG2Bj18eOsv7v\ngf+grH1X13WOsvZL9RywH9gLfAD4mnxuEcprVzFwoxXXZOvXTXt9LbG355cf8B7K/z9FwLU2XtMi\nlN9ZIZANuFp5PQP9+znYz6+e1mOPz3ebGoGyzTAGGIljnAu5HriK7r/YvwKPd11eCPzF2ovqp1Dg\nyq7LXijbPONxnPV7dP3rDHwJpOA4a1c9CqwDPu762FHWfwTlBdWUo6z9Uv2Uc5X2f+Hcz/kjlNes\nkSivYSVYpyLfHl437fW1xN6eX/8A5nZddkb5o2+rNY0BSlGCM4B3gNlWXs9A/n5a4/nV03rs7flu\nc0nAZpOPf9/1n70bQ/dfbDFwWdfl0K6PHcGHwA043vo9gK+BOBxr7aOAfwFTOfeO31HWfwQINLvO\nUdZuSenAW12XF9E9m7UZpXp0sNnj66Y9vJbY2/PLFyUwMmerNQWgBNT+KEHjRpSgxNrrGUP//n5a\n6/llvh5Tl/R8HypR3FBpMnkZSvqUrn8v6+O29mIMyjuJr3Cc9TuhvKM5ybltF0dZO8CLwO9Q2j6o\nHGX9nSh/BHcD93dd5yhrt6S5wKddl/Uor1kqa71+2dvr5hjs47XE3p5fkUAlkAUUAP8LeNpwTdXA\n34BjQDlQi7LlaOvncW/3b6vnl6lLer4PlUBtKDaZ7MT+fy4v4H0gE6g3+5w9r78DZbtlFDAZ5Z2z\nKXte+83AKZTzM731QbTn9f8Y5Y/xdGAeypaBKXtee3/8E+Vdtfl/t5jcZjHQinK2pzfWeAzs6XG2\nl9cSe3x+OQMJwN+7/m3g/MynNdc0FngYJbDWo/zu7rHhenpyofu35tou+fnubNHl2E4ZyqFUVQTd\nI1ZHcRIlZWsEwlBeMOzVSJQX1rUo2xXgWOsHOAPkApNwnLUnA7cCP0MpjPBB+R04yvoruv6tBHJQ\nZmM6ytr746cX+PyvUH53PzG5zvz1a1TXdYPNXl437em1xB6fXye6/vu66+P3ULbPjDZaUyKwA6jq\n+vgDlG10W61H1dvvyFbPL7DQ832oZNR2A+M412RyFucOgTqSj1EOZdL174d93NaWdMDrKNVHy02u\nd4T1B3GuGsgd5Q/rNzjG2gGeQHmSRwL/BWwFfoljrN8D8O667IlS7VSIY6zdEm5C2VKbATSbXP8x\nyu/SBeX3Oo5zFbGDyR5eN+3ttcQen19GlC3qmK6Pb0A5rrHRRmsqRjlT5Y7y+7sB5fdnq/Woevsd\n2er5ZW/Pd7vgaE0m30bZ329FeRLOQTmk+S/sv01BCsr24bcoQc43KP9TOsL641HOeXyL0ibid13X\nO8LazU3h3B9WR1h/JMrj/i1KKwb1eeoIa7eEQ8BRzj1n/m7yuSdQXruKgTQrrsnWr5v2/FpiT8+v\niSgZNdNWD7Zc0+Oca8/xD5SsqDXXM9C/n4P9/DJfz1zs8/kuhBBCCCGEEEIIIYQQQgghhBBCCCGE\nEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQYjBcjTJRwBVldNp3wI9suiLhUHS2\nXoAQ/TQdZU5nBMow70aU8RxCCGHvlqIMeXdHGTG0zLbLEUIIy7ocWN91OQBYC6TbbjlCCDEgI1Gy\nal8iCRIxQE62XoAQ/TAbWNd1uRplK6HKdssRQogBCULZ9vRCyaoJ0W8SqAlH4AIc67rsATQAn9tu\nOUIIMSCvAkuAbGTbUwzQCFsvQIh+OAr8DGXbcwznDuUW2XBNQgjRH/cCY4E/Al8AfwBKgO9tuCYh\nhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIMN/8P\nSi8Y+xQVR8QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6e97103ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extract the traces and plot the results\n",
    "pymc_trace = [S.trace('alpha')[:],\n",
    "              S.trace('beta')[:],\n",
    "              S.trace('sigma')[:]]\n",
    "\n",
    "plot_MCMC_results(xdata, ydata, pymc_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "结果和emcee很相似。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyStan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[PyStan](http://mc-stan.org/pystan.html)项目是C++实现的[Stan](http://mc-stan.org/)概率编程语言的Python封装版。使用[No U-Turn取样器](http://arxiv.org/abs/1111.4246)，比Metropolis-Hastings和Gibbs取样更复杂。不考虑API，PyStan与emcee和PyMC的差异是，它要求在Python程序内**编写并编译非Python编码**。\n",
    "\n",
    "因为PyStan依赖Stan包，安装很困难。为了用Python封装版需要安装全部的Stan库。如果你有C/C++编译环境，直接``pip install pystan``就可以搞定。\n",
    "\n",
    "好像Stan也提供已经编译版本，支持conda。因此，如果你没有C/C++编译环境，安装可能比较麻烦。\n",
    "\n",
    "我用的PyStan 2.5版本："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5.0.0\n"
     ]
    }
   ],
   "source": [
    "import pystan\n",
    "print(pystan.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "还有一点诡异的是：PyStan在IPython notebook上运行容易崩溃，直接执行Python文件就没事。不明觉厉，但是[这里](https://github.com/stan-dev/pystan/issues/3)可能是解法。所以，安全起见，我直接在命令行运行Python文件，结果写在盘里："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing pystan_example.py\n"
     ]
    }
   ],
   "source": [
    "%%file pystan_example.py\n",
    "\n",
    "import numpy as np\n",
    "import pystan\n",
    "\n",
    "#---------------------------------------------\n",
    "# Generate data (same as used in the notebook)\n",
    "\n",
    "np.random.seed(42)\n",
    "theta_true = (25, 0.5)\n",
    "xdata = 100 * np.random.random(20)\n",
    "ydata = theta_true[0] + theta_true[1] * xdata\n",
    "\n",
    "# add scatter to points\n",
    "xdata = np.random.normal(xdata, 10)\n",
    "ydata = np.random.normal(ydata, 10)\n",
    "\n",
    "#----------------------------------------------\n",
    "# Create the Stan model\n",
    "#  this is done by defining a string of Stan code.\n",
    "\n",
    "fit_code = \"\"\"\n",
    "data {\n",
    "    int<lower=0> N; // number of points\n",
    "    real x[N]; // x values\n",
    "    real y[N]; // y values\n",
    "}\n",
    "\n",
    "parameters {\n",
    "    real alpha_perp;\n",
    "    real<lower=-pi()/2, upper=pi()/2> theta;\n",
    "    real log_sigma;\n",
    "}\n",
    "\n",
    "transformed parameters {\n",
    "    real alpha;\n",
    "    real beta;\n",
    "    real sigma;\n",
    "    real ymodel[N];\n",
    "    \n",
    "    alpha <- alpha_perp / cos(theta);\n",
    "    beta <- sin(theta);\n",
    "    sigma <- exp(log_sigma);\n",
    "    for (j in 1:N)\n",
    "    ymodel[j] <- alpha + beta * x[j];\n",
    "}\n",
    "\n",
    "model {\n",
    "    y ~ normal(ymodel, sigma);\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "# perform the fit\n",
    "fit_data = {'N': len(xdata), 'x': xdata, 'y': ydata}\n",
    "fit = pystan.stan(model_code=fit_code, data=fit_data, iter=25000, chains=4)\n",
    "\n",
    "# extract the traces\n",
    "traces = fit.extract()\n",
    "pystan_trace = [traces['alpha'], traces['beta'], traces['sigma']]\n",
    "\n",
    "# save the traces with numpy\n",
    "np.save(\"pystan_trace.npy\", pystan_trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_c1dba2ed7f485b674d7ce5eb738ffe05 NOW.\n",
      "Iteration:     1 / 25000 [  0%]  (Warmup) (Chain 3)\n",
      "Iteration:     1 / 25000 [  0%]  (Warmup) (Chain 2)\n",
      "Iteration:     1 / 25000 [  0%]  (Warmup) (Chain 1)\n",
      "Iteration:     1 / 25000 [  0%]  (Warmup) (Chain 0)\n",
      "Iteration:  2500 / 25000 [ 10%]  (Warmup) (Chain 1)\n",
      "Iteration:  2500 / 25000 [ 10%]  (Warmup) (Chain 2)\n",
      "Iteration:  2500 / 25000 [ 10%]  (Warmup) (Chain 3)\n",
      "Iteration:  2500 / 25000 [ 10%]  (Warmup) (Chain 0)\n",
      "Iteration:  5000 / 25000 [ 20%]  (Warmup) (Chain 1)\n",
      "Iteration:  5000 / 25000 [ 20%]  (Warmup) (Chain 2)\n",
      "Iteration:  5000 / 25000 [ 20%]  (Warmup) (Chain 3)\n",
      "Iteration:  7500 / 25000 [ 30%]  (Warmup) (Chain 1)\n",
      "Iteration:  7500 / 25000 [ 30%]  (Warmup) (Chain 2)\n",
      "Iteration:  5000 / 25000 [ 20%]  (Warmup) (Chain 0)\n",
      "Iteration:  7500 / 25000 [ 30%]  (Warmup) (Chain 3)\n",
      "Iteration: 10000 / 25000 [ 40%]  (Warmup) (Chain 1)\n",
      "Iteration: 10000 / 25000 [ 40%]  (Warmup) (Chain 2)\n",
      "Iteration: 10000 / 25000 [ 40%]  (Warmup) (Chain 3)\n",
      "Iteration: 12500 / 25000 [ 50%]  (Warmup) (Chain 1)\n",
      "Iteration: 12501 / 25000 [ 50%]  (Sampling) (Chain 1)\n",
      "Iteration:  7500 / 25000 [ 30%]  (Warmup) (Chain 0)\n",
      "Iteration: 12500 / 25000 [ 50%]  (Warmup) (Chain 2)\n",
      "Iteration: 12501 / 25000 [ 50%]  (Sampling) (Chain 2)\n",
      "Iteration: 10000 / 25000 [ 40%]  (Warmup) (Chain 0)\n",
      "Iteration: 15000 / 25000 [ 60%]  (Sampling) (Chain 1)\n",
      "Iteration: 12500 / 25000 [ 50%]  (Warmup) (Chain 3)\n",
      "Iteration: 12501 / 25000 [ 50%]  (Sampling) (Chain 3)\n",
      "Iteration: 15000 / 25000 [ 60%]  (Sampling) (Chain 2)\n",
      "Iteration: 17500 / 25000 [ 70%]  (Sampling) (Chain 1)\n",
      "Iteration: 15000 / 25000 [ 60%]  (Sampling) (Chain 3)\n",
      "Iteration: 17500 / 25000 [ 70%]  (Sampling) (Chain 2)\n",
      "Iteration: 12500 / 25000 [ 50%]  (Warmup) (Chain 0)\n",
      "Iteration: 12501 / 25000 [ 50%]  (Sampling) (Chain 0)\n",
      "Iteration: 20000 / 25000 [ 80%]  (Sampling) (Chain 1)\n",
      "Iteration: 20000 / 25000 [ 80%]  (Sampling) (Chain 2)\n",
      "Iteration: 15000 / 25000 [ 60%]  (Sampling) (Chain 0)\n",
      "Iteration: 17500 / 25000 [ 70%]  (Sampling) (Chain 3)\n",
      "Iteration: 22500 / 25000 [ 90%]  (Sampling) (Chain 1)\n",
      "Iteration: 22500 / 25000 [ 90%]  (Sampling) (Chain 2)\n",
      "Iteration: 17500 / 25000 [ 70%]  (Sampling) (Chain 0)\n",
      "Iteration: 25000 / 25000 [100%]  (Sampling) (Chain 1)\n",
      "\n",
      "#  Elapsed Time: 0.608499 seconds (Warm-up)\n",
      "#                0.684071 seconds (Sampling)\n",
      "#                1.29257 seconds (Total)\n",
      "\n",
      "Iteration: 25000 / 25000 [100%]  (Sampling) (Chain 2)\n",
      "\n",
      "#  Elapsed Time: 0.620206 seconds (Warm-up)\n",
      "#                0.72414 seconds (Sampling)\n",
      "#                1.34435 seconds (Total)\n",
      "\n",
      "Iteration: 20000 / 25000 [ 80%]  (Sampling) (Chain 3)\n",
      "Iteration: 20000 / 25000 [ 80%]  (Sampling) (Chain 0)\n",
      "Iteration: 22500 / 25000 [ 90%]  (Sampling) (Chain 3)\n",
      "Iteration: 22500 / 25000 [ 90%]  (Sampling) (Chain 0)\n",
      "Iteration: 25000 / 25000 [100%]  (Sampling) (Chain 3)\n",
      "\n",
      "#  Elapsed Time: 0.610114 seconds (Warm-up)\n",
      "#                0.657225 seconds (Sampling)\n",
      "#                1.26734 seconds (Total)\n",
      "\n",
      "Iteration: 25000 / 25000 [100%]  (Sampling) (Chain 0)\n",
      "\n",
      "#  Elapsed Time: 0.616008 seconds (Warm-up)\n",
      "#                0.687802 seconds (Sampling)\n",
      "#                1.30381 seconds (Total)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# run the code we've created on the command-line\n",
    "!python pystan_example.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看到，运行100,000样本约6秒。另外，在我的电脑上，模型运行前有约20秒准备时间。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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obID95RBROYFAcC3S0tJCRUUFdXV1Toui5ebm8uqrr1JXV8fDDz/MzTfffNU3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\n02OYjGyZtN8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6e73863b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load the results from file; plot as above\n",
    "pystan_trace = np.load('pystan_trace.npy')\n",
    "plot_MCMC_results(xdata, ydata, pystan_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可见，结果和上面都差不多。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 总结：结果比较"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "下面我们画图来比较一下三个结果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uygXdVEWp8m3x4sVO7xctWoSfnx/h4eGAtR+7f//+zJo1i3nz5vHoo4/a+8JdeXt706VL\nF1588UVOnjxpH/BWqVIl/v7773zpT506RYUKFZw+++9//0teXl5xXNpV0z5yVS7owDelyrekpCTy\n8vKIjIwkNTWVuXPnMmHCBPz8/Oxphg0bxuzZszEYDE7N6gDvvvsu69at4+677+aGG27g8OHDTJky\nhTp16tC8eXMAmjVrxpw5c3j33Xdp06YNlStXJjw8nJ49e7Js2TJGjx5Nr1692Lx5MwkJCQQEBJSJ\nDWo0kCullCrzli1bxnPPPcekSZMICAjgtdde47XXXnNK06JFCxo0aEBgYCCtWrVy+q5Vq1akpKTw\n8ssvc+jQIWrUqEHHjh1ZuHChfZrZU089xffff88rr7zC0aNHufnmm/n99995+umn2b9/P++99x6z\nZs2ibdu2LF++nD59+th2JbNzfW/7zN3nxUW3MVVXROdwK1U2lbdtTGNjY5k4cSK5ubl4eRXeG7xj\nxw6aNm1KUlISgwcPvkYlLB5Xs42p1sjVFdEgrpQqK8xmM7t27WL8+PEYjUZiYmJKu0jXlA52U0op\nVWYVpVl6zpw5dO3alaysLJKTk+1N5dcLbVpXSqlypLw1rV8vrqZpXWvkSimllAfTQK6UUkp5MA3k\nSimllAfTQK6UUkp5sGs9/awHMA2oACQB8S7f1wQ+BEKwlu3fwPvXsHxKKeXRAgMDS3TxEVUyAgMD\nr/jYa/nXrgDsALoBZmAT8Ciw3SFNLFAJeBlrUN8B1AZyXfLSUetKKaWuG2Vl1HpbYDewFzgHLAJ6\nu6Q5CPhf+N0fyCZ/EFdKKaXUBdeyab0OsN/h/QHgNpc0c4BvAAvgBzyCUkoppQp0LQN5UdrCXwF+\nBqKA+sBXQEvghGvC2NhY++9RUVFERUUVQxGVUkqp0rdmzRrWrFlTpLTXso/8dqx94D0uvH8ZyMN5\nwNsKYDLw3YX3q4CxwGaXvLSPXF2VsWPHEh/vOtZSKaXKpsL6yK9lIK+IdfBaV6xN5z+Sf7DbVOAY\nMAHrILc0oAVwxCUvDeRKKaWuG2VlsFsu8ByQCvwKfIQ1iD9z4QXwBhAJbAG+BsaQP4grVawsFktp\nF0Eppa6Yp0421Bq5Ukqp60ZZqZErpZRSqphpIFdKKaU8mAZypZRSyoNpIFdKKaU8mAZypZRSyoNp\nIFdKKaU8mAZypZRSyoNpIFdKKaU8mAZypZRSyoNpIFdKKaU8mAZypZRSyoNpIFdKKaU8mAZypZRS\nyoNpIFeXRbf8VEqpskW3MVVKKaXKON3GVCmllCqnNJArpZRSHkwDuSo1JpOptIuglFIeT/vIVZll\nsVgwGo2lXQyllCp12keuPFJZCeI6Ul8pVZZpIFdlQlkOlmXlgUIppdzRpnWllFKqjNOmdVUu6OA4\npZTKT2vkSl3HdEChUp5Ba+RKFUFZ7qcvKRrElfJ8WiNXSimlyjitkSullFLllAZypZRSyoNpIFdK\nKaU8mAZypZRSyoNpIFdKKaU8mAZyVWqKe7rX9Th9TCmldPqZUkopVcbp9DN1XUtNTS3tIiilVInR\nQK7Kvejo6GLLq6QfCrR7QCl1ubRpXZUbum64Uqq8KqxpXQO5UkopVcZpH7lShdA+dKWUJ9NArsq0\na9FnfDV96PoQoJQqbRrIVZlW1vu8o6OjixTMdRCbUqqkaB+5Usotk8lEREREaRdDKYX2kavrmNaE\nr5xrENd7qVTZpDVyVSJ0KphSShUfrZGra64sBfFrUZMsz4PetCauVNmmNXJVbhXUKqB9v0opT6M1\ncuWxEhMTr/jYgloFrkUQL4+1WJPJVNpFUEq5oYFclSmOTdQmk4nhw4df8pjk5OSSLNIVKUtdC8VF\nWzGUKpu0af06ogPQrPcgMzPTbVC6mvuj91YpVZK0aV0B5bOWeLmMRqNTEJ88ebLTd5fDsfm8OO9t\neWyWV0qVHK2RK490rWrAOjBOKVUW6O5nSimllAfTpnWlSpE2lSulSpIGclVuXO30KFvAvZrA6+5Y\nHZuglCpJ2rSuyqxr0Q9eEufQEexKqeKmTeuqxJRks7HRaMy39Onlnu9S6Usi4GoQV0pdS1ojV+oy\naG1bKVUatEauVDHJzMy84mOvtg+/LC2RqgP4lCo7tEaurlupqalER0eXdjGUUuqStEauStW1qr0V\nVmN1t82ouyB+rdZtdyyr1m6VUldDA7kqMbZgdbV9ykUNdI4rsLkeU1DN2zVwh4WFXWbp3LtUM7hj\nWbXPXSl1NTSQqxJTXEubuga6ogT2ogbHmJgYp/e2MrsG+NTUVHtwLsr5L+fa3bUWOCqtGntZ6pNX\nShVM+8iVRymNUeNFWW/9ctZkT0xMtG/POnnyZMaNG3fVZVRKlW+61roqV9wNUiu1aWGbN8PGjdC5\nM4SHg+HK/5Mq6GFAN25RSulgN1WuREdH52v2vdogXpRmZHsTd24uLF4Md9wBt94KL7wALVtaA/mU\nKbB3b9HycVFQs74GcaVUYbRGrkqVyWQiJCSk2GrTRZlSdrm198TERBo0aEB0ZCTMmQOJiXDggPXL\n6tWhe3f45hs4cuTiQXfcAf37w8MPQ82aV3IphUpOTs7Xv6+UKr+0aV2VuMtp/i2upuIrCWZX1AS/\nbRtMn07WJ//lk1tOUyEPAmsYCez1IAH3PszZMxUJq3ML1df+gNfCRfDZZ/D339ZjK1aE6GgsPXti\nHDQIfH0veTrbw8jVdhfoKnRKlR8ayFW5VWKLuuTlwYoVMG0arFrFr8FwV28w3wBYADfx0YCB6pWr\nE1gpgMDTEHjoBIHmbAL/xvo6701Ak1YE3n4ngW07EVgtmLNHz3J7k9v5+quviY6OLjc1bccBfUqp\nq6eBXF21kqzdXW0N3bVsl1tWp/THj2OaNImIzz6D3bsBWB1WiT6PCMf+OkvzWs1pG9aWnNM51tff\nF3+eOHviQoa4DfRuHYfG9Rozr/c82tVtV+Qyuy27Uqrc0kCuyqXLfQAoNP1vv8GMGfDee3DCGpAt\ndeowtXt93rllI+fyztEnrA8fPvAhVb2rus0iNy+Xo6ePcvT0UXL+zmHT5k0E1Q+yB/qMjZvwOf0H\nv5t+5Yz335wKggP+kOULBoHRjQYy6eH/UMW7SrFcb3HQEfNKlQ0ayJXHKK4m2SI1UYtYB6lNnw6f\nf259D9CpE/LCC0yqkc74tRMAGNJwCDP7zeTPzD+LVAMuNACKwJYtkJzM6cXJTGhg5s07IM8LGp2o\nxLyaT3Jz10EYb73VfojWvJW6vun0M1WmOU7HCgwMzPeZo6KuNlZoEBex1rxbtIBu3WD5cvD2hkGD\n4KefOPvNV/Q99hHj107Ay+DFjJ4zmBUziwpeFezB1HGKmLuy2oK42+swGDDl5cGbb/Ltf+Yw5bU1\nbDzcm6bZXuz0O0OH0zOZ+mpb/r6zI8ycCb/+ypo1a674XiilyjetkasyoThrnJfM66234J//tP4e\nEoJlwACML75I6k8/cVvn23hw8YN8s+cbqnpXJbFDIoM6DcqXd0E17oLObfvn6rhejGsep08eY8IH\nT/Lmn5+QZ4BGh2HeMmi/HyxhYRgHDoR+/bD4+FzT2rm2BihV+rRpXZWokvgffYmNRrdYsDRsiPHU\nKUhIgKefBh8fAPYd3cfdyXfza9avhFQL4fNHP6eNsc0VnyotzcKWLUZWroSvvoIzZ1Jp0yaaKlWS\nefjhGFq0sK4h4zojbZN5E4M+fZxfj2TAcRi9uxLDvjhD/fMXErRvDzEx1jnqtWoVuTza362U59JA\nrjza2LFjiY+PL57M+veH5GS4/35YutT+8WbLZu5deC+Zf2XSNLgpK2JWkPFDBtHR0fkeKhwfXBx/\nP3sWNmyAlSshJQV++cX15Lbh7BeHtRsM0KCBdWE4x1eu7OHt76cyc8dM8iSPRpXq8N7OMO5YtOHi\nHPUKFaxdAzEx1uvx9y+ee6SUKnM0kKtSU6ZqgWvXWtdEr1wZtm+Hm28G4P217zN8/XBOnTvFnfXu\n5JNHPiGgcgDgPmg7XtOmTRZWr4aNG42sWmUf8A5A1arQtSv06GF9VatmHePm+Nq+HXJzU4FoHAN8\n9eoWWrUyEhKxiTXeA/iz6k5r7bzLc0w6GkHVRZ9Aaqp1uViwXtM998Cjj8Ldd1vfK6XKDQ3k6rpl\nD7q5uRARQWp6OtETJsDrrwOQ+GMiL6S8QJ7k0e18N74Y/wU+FXwKzO/MGVi37mKt+9dfnb9v1swa\ntHv2hA4doFKlwrsezpyBuXNT8fWNZssWay1+yxY4fNh+BVChGXSeCC3/D6rnUetIXT79x0Lu8A2D\nJUusLQxr117M1N8fHnzQGtS7dLGuLqeU8miFBXJPJUqJiKSlpRUt4fTpIiBSr57IqVOy/8B+6Z/Q\nXxiCEItMWDNB8vLy3B76++8iiYki99wjUrWqCJjFOnxNxM9PJCoqTWbNEtm3z/m4hISEfHmZzWZZ\nsGBBodeSlydiNousWCEyZYpIv34iTZqIGOpsEoY1E2IRQ6xBnvzwaTl59qT14D/+EPnXv0QiIsRe\nOBCpXVvk+edFNm60ZqyU8khAuau9lvY9VcXAbDYXKV1KSspl5ZsvuGdmivj7WwPbsmVy8uxJeeCj\nB4RYxHuit8z/eX6BZXvuuTSBtAtx0fqzZUuRsWNF1qwROXOm6OVyF9gLK7/ZbHa6lpMnRV58+bTQ\n9RXh9QrCEOSWtxvK+n3rJS0t7eL93L5d5PXXRRo2dA7q9eqJvPKKyNatRS+0UqpMQAO5Ko8ef/xx\n+++FPRSYH3lE0kDk7rvlzxOZctuc24RYpPqU6rLq91UFHjdxoq32nSIPPSTy3nvWmrLbc1z4wt1D\nR1EfWApKn5aW5lSL//JLkcBmm4RuRmG0tXY+KmXUxdq5TV6eyKZNIqNHixiNzkE9PNxa3d+z57LL\nZyuTUuraQQO5up44BpkFCQnWwOXjIxmbU6TuhLpCLHLT2zfJtkPb3B5rNpslNtZ6mMEg8sEHRTuv\n2Wx2GxQLC3qO6RcsWOBcsy7EwYMiXbqdFu54wVo7j0UaTG8g3+791t5FYHuoSElJEcnNFVm9WuTp\np0UCAy8GdINBzKNHS9qmTUW7yMtQUBeCUuryoYFclTVXW6Mr8vH//a+YQfLu7in14+oLsUiTcU0k\ndV2q2+R5edZWaRDx8hL58MOCz20LuLYAnpKSYv+uqAH5UtdhC8bu8srNFRk6NM3adz60uRBr7e9v\n+E5Deemrl2STeZP7fv8zZ0T+9z+Rvn2tTyog0quXyJEjlyyvUqp0oIFcXUtF7Qt2dDnNu5eq6Tnl\n9cQT1kD1r39JxYkVhVjkyKkjToHW9jMvT+TVVy8G8eTk/HlfKvDaArojx/vheHyh3QEO+djSpaWl\nub23r722QOrceFqIfEroWMke0G0tD6NTRsuGPzbI+bzz+U+UmipSo4b1ouvXF/nll0KvTylVOigk\nkHvqUPYL16WuNwUtxlJgunr1YO9e2LyZgK+6cuzMMbLHZFOjSg2n9CLw6qvwxhvWdVYWLIC+fS9d\nhsK+L+459I4L0ziWwWQycdNNEQweDMuXr4Cbq9C87xIO1/yUzJOZ9uONfkYeCHuAh5o+RIcbO1DB\nq4L1i7174YEH4KefrJPfk5KsU9eUUmWGbpqiyg3HAOq4kUhqamr+dHv3Wl8BAdCqFb4+1rVQT549\n6ZRWBF555WIQX7gQOnZ0v2mLaxkKYrFYClyL3d3vkH8TFNfvHVeXc7z2kJAQzpyxMGxYKtOm3Y23\nuQtb4++g9gIzyd3WM/K2kdT1r4vlhIWETQlEzY/CONXIM8uf4avfvuJc3Trw3Xfw+ONw6pR1pbjR\no+HcuQLLopRSV6u0WzlUMbiS0dKXlcd774kZRHr3FhGRhu80FGKR7VnbZcyYMSJibU4fM8baslyx\nosiSJZd/fqdBZZcol2tzvmOfumMa13SOFixY4PS5a5pJkxZI/frWEfe+viKTJqVJXl6e/HDgBxnz\n5RipP72+U/N7jfgactfrd8nnGcvldMI0640Akc6drVP3lFKlDu0jV9ebtLQ0kQEDrAFp2jQREWn1\nbishFkmzXFx4ZcAA69zwChXM8sknRchT8gfdS/WbX+nAPteHhIIG0KWkpOTrl8/IMEu/fiKQIiAy\naJDIX38E70PCAAAgAElEQVRZv8vLy5OfDv4kr656VcISwpyCuv8Uf+nzf53k09sD5FRFROrUEfn+\ne3t5lFKlgzIUyHsAGcAuYGwBaaKAn4CtwJoC0pT2PVUlqKDgeFmBJC/PGoRA5JdfZMGCBXLH3DuE\nWGTt3rWSlycyapR1kRdvb5GlS/NnYSuDbVqYu+8KKltBZbUNVnMdyGb7GRcXZw/YtnO4q/HbjnH9\nzHHkfF6eyJw5IlWqWAN6WJjIli35y7Tt0DaZuGaitPhPC6eg7vuqlzz8MPJRywqy5/8mF3pdSqmS\nRRkJ5BWA3cDNgDfwM9DEJU0AsA244cL7mgXkVdr3VJWiguZrO9m50xrEa9YUOW8drX3Xf+8SYpGV\nu1bKs89al1n19hZ5662Cg7ItiBcUTF3ZRtQX1PRtK7tr7drx97i4OLd5F/Vhwcb20LBqlVmaNrUG\ncx8fs7zyisi2/FPoRURkV/Yu+b91/yeRsyOdgvptTyF/Ph0j8vffhZ5TKVUyKCOBvB2Q4vD+pQsv\nR8OAiUXIq7TvqSojUlJS3Ae4d98VATH36mX/vM+iPsJo5ONtS6RCBWuc//RT63ddu3Yt9BxFYTab\nnWrcjscV1LzuWiN3nXbmLljbAr3j9wkJCU5T01zzPXlS5MknnRd3a9dOJClJ5MQJ99e5N2evTN0w\nVW6MCxJikXojkO2dm4ns23fZy+Yqpa4OZSSQPwTMcXg/AJjhkuZtIAFYDWwGHisgr9K+p+oaKKjG\nWdgyqPaA2bevNVrNnGlPM+DTAUIsMv/n+fZlyG1Nze7OZas5OwbhhIQEpyBZ0Nxud1zzsgVt1+Md\n07hr0nd9QHAM/CkpKYXOs//qK2tA9/O7GNCrVRPp188sGza431fl4ImDEjmtqXVZ22HIty2qi6wq\neGnb4nIl6xEoVV5RRgL5g1w6kCcAG4AqQBCwE2joJi8ZP368/bV69erSvseqFOXrOz5wQKRWLWuU\n2r7d/vkzy58RYpGZP86U+++3NjU7Lvpiq+E6BvWC+sYLa9Z2bDYv6oh2x5HotlYGd2uu2346lsO1\nVcK1Nu4usP/1l8i8eSIdOojAUHtQb9pU5K23RA4dEqf8/jrzl9w3v4cQi/i8inzYwmDdba0IO6pp\nv7pSl2/16tVOcY4yEshvx7lp/WXyD3gbC8Q6vE/CWpN3Vdr3WJUxKSkpEhcXZw2YW7dao1JIiFOg\nGbJgiBCL/Ou7f8m4cdYkL7yQP9jZfi9seVSbggJuQc3qhf1e0Gj4wh4eHD8r6GHhUn3r27eLvPii\nSFDQxe1Zvb1FHnpIZOVK61KwIiK553PlhS+et/ebT+qE5D3y8MW2eRe6sYpSxYcyEsgrAr9hHezm\ng/vBbmHA11gHxlUF0oGmbvIq7XuqStEl+2dnzLBGo5gY+0dms1lGfDRCiEViV8fKwoXWJBemmNvT\nFKSgmq9tPrq7EeWuedqail2DtmO+jr8Xtgua6+A41zxt3I24L8jZs9YxA716WZeohQQBkbp1RUaN\nMsuePdZ00zZOE0OsQYhFBvdGzjZvKrJjh9s8i9KCoZS6NMpIIAfoCezAOnr95QufPXPhZfNPrCPX\n04EXCsintO+pKsv69LFG6TlznD6esm6KEIu8+OWL8ssv1iQNGjgfWthDguPAsqIorIneVVpamvTq\n1avQpvLCpuTZvrNt7RoXF+e2Jl7Utd737xeJixO58caLtXSDQaR7d5GXXkqRxb8slSqTKguxSLfH\nkKM1/USWLSv0GpVSV44yFMiLS2nfU1VGpaWlXZw/vm6d/fOUlBR55/t3hFhk2OfD5MwZ6wJmBoN1\nRHdRArjZbM63qppjGlvfuK2W7i4P2++uU9Acj3Eti2M62+9ms9nt6HXXpvarrQmfP28d1xYTI1Kh\nwgJ7UPf3T5OBL/8oteKDhVik2TBkb3VEHn1UZN8+t9evtXKlrhwayFV5VGBgsC5pJtKkicjRo/aP\n55rmCrHIwKUDxWw2S5Mm1mSXanl2VxNPS0tzO2WtsAcCd4vIuAbpwtLb8ncsh2PfvmMztruBe+5W\ngCvsXLa8bBYvTpEZM0Ratrw44j3yzo3SeHoTIRYJ+SeyORSRypVFXnutwL5zpdTlo5BArpumKI9V\n4OYls2ZBs2ZYtm+Hfv0gNxcAX+8Lm6acO4nRaKR5c2vybducD09MTLzkuSMiIvjggw8A5w1FHHcn\ns1gs9rxcd0IzmUzMmzePkJAQ0tPT7Xk6HuuYPjU1FYvFQnBwMNu2bSM1NZXExESioqLs58/KyrL/\nnpmZSXp6un1zFYvFQnR0NMHBwW43QClolzbHe/zww9E895x1k7Rvv4XatWHzN7djmPcdt4dEkVkN\n2neBz288DZMmQePG8Mknl7yXV0s3dFHKM5X2w5EqQ9yO0P79d+uqbiAycqSIiCzfsVwYjfT8sKeI\niMTGWr+2tWoXNGq8oMVabNwNXCusWbuggXEiF2vYrrXrwkbQu9bsXaedFXUFOMclaYti9Og4e6tG\nbeMZ6ZX0mBCLeMV6ScKDda0L8oBIYmKR8lNKFQytkavyzLHWaP+9Xj349FPw9oZp02DOHGuN3N9a\nIwdo1gzAYq+RR0RE2Gt3RqORiIgIUlNTSU9PL3QPcttxkydPttfIg4ODiYuLy7c1KcDu3bvzbbtq\nExMTg8ViISsrC5PJZK9Zh4eH28sCF2uhJpPJXi6j0WgvZ3Jysj1P2zH33HMPAJMnT3Y65/Dhw+2/\nm0wmYmJi7O8Lq+2+9dY4Ro5MJioK/rT4sHrEfGKM48kjj+fC9/OPSR0IMQDDh8ObbxaYj1Lq6mgg\nV+WKU7N4x44we7b193/8A1+pCFj3I7dYLBea1o1s2wZjx7rfwyc8PJzdu3fbg2R4eDjg/PBgsVjI\nzMxk3LhxpKamYjQaycjIoFmzZvYma8fA2qdPHzZv3gxgD9aOAdNoNBIdHU1ISAgZGRkEBwfbyxIe\nHs7kyZNZunQpYN2L3NYMbzKZWLNmDSaTiaioKKKiokhOTrYfP3v2bEwmE+PGjbOfz/GBIiQkxKmJ\n3fWhwN3DR7VqkJICAwbAqZMGFj0by+P+71PRqyJTz6/noTdacaISMHYsvP66tWtdKVWsDKVdgCt0\noaVBqSJo0wZMJnZ9NJNG24dRs2pNDv7jIORVxNcXzp61cOKEkWrVrMkLqn071tYL+zwxMdFey7X1\njTvmmZycTFhYGCEhIfbPbDV3x1aB9PR0oqOjGThwIPPnz8dkMpGVlUVwcLA9XWZmptNnruVxrVHb\naue2loPLkZycbG8xSE9PJzs7234doaFGxo+3do0D9H3pG1KqP8CxM8e4pWIt3p55iPsswMiRMHUq\nGK7sfz2FtYwoVZ4ZrP/NeGrMdqu0uyuUB7D3DU+ZImaQvP4x0nhGYyEW+XzH5yIi0qSJdZ70/Pnu\nF1QpqH/Z1m99qVXXXEeOO45QT0tLs08hczf63DbVzXbM0KFDnfK3LRBj6z93XAnOcc11d33ejtPY\nXMvnbvOVwtim5YmIzJ1rndYHIj0GbJeWM617wFeI9ZLxd3rJOS9Ennrq4nJxl0Gnr6nrGdpHrsqz\ngvpx7TW3hx/GCBj+t5yBzfoDMH/LfABatbKmyc2NcKoNg7UGWljtLzg4mJCQkELLlp6ejtFotDdL\nZ2Zm2r+LiIhg3LhxwMW+cVsz+cCBAwkLCyMzM9NehpkzZ5KcnOzUfRAVFWWvXdv69G1lchzRbrtP\nw4YNIzExkaysLKe8LRaLvWneJjU11V7ewvrKjUYjQUFBADzxBKxYAX5+kPJhGBXnfcrzEWPIQ5jQ\nKY8OTxrY/WkSPPYYnDtX6L1zdx6lVPlR2g9HytO0bi0Csv/juWKINYjPJB/JPpUtcXHW2uPo0c7J\nHWvaBc3vdp1X7vjTxnUBGXej3V1Hqtvydq0dO5bH8XyOedpq7QsWLJAFCxZIQkKCPb27RWMWLFjg\ntApcYQu3jBkzpsANX1z98otIaKi1taNhQ5H/rv9Gbph6gxCL+L6CvN/ywvq4F/Y313XZlSocWiNX\n5Zm7keH50rRvD8ANy1bTvX53zp4/y6KtiwqcS75y5UoA1qxZk28AmG2AmeNob1tt3pbWZDLZ+5Qd\n+8Ed+61tx0RFRdn70k0mE6mpqbRr1w6Adu3aOQ0yW7NmDRkZGfZR7Y797AAdOnQAICwsjKCgII4e\nPeo0iM12r2w/9+zZw7hx4+x95wX1/wPEx8e7rRU7jnK3CQ+H5cuhVSvYtQuejT5IUptf6NusLyd9\nYFAfmHB0GXLfvXDyZIHz2JVSl6aBXHm8ogSBiJEjATB9+ikDmz4KWJvXrVPQ8j8MjBs3zj4VyxZc\nwRrobC9XttHntgCbk5Nj/84W5G35JCcn24Pk0qVLnR4EsrOziYiIYN68eWRlZdmnq6WmphIVFcWe\nPXsA6wIwtrLbXjYhISFER0fTs2dPp2lptib1rKwskpOT7SPYbaPxbQPoXEeoF+VhyVWbNkbWroUe\nPeDkyRjujw7kziNvMeueWXjhRWwX6Hfya/J6RMOxY5fM70rKoJQqu0q7lUN5ogvN6yeXLhb/Kf5C\nLPLLwW1SpYq1eT0rq+iD1hw3KXHXBG5rznbdqtR1MRjH97adyhwXlLE1pdu+c2zyt53TcQnZ0Ymj\nZdBngyQxOdFpQJtjmW2fu3YRJCQkuN1+1bXZu6AlYh2/czzm3DmRIUMuLuv65JMi7//wqfhM9BZi\nkZgHkLORESKHD4tSyj10rXWlROSNN6yRZMAAefp/TwuxyJgvx8hdd7ndLM2JuwBf0Cj3tLQ0ex+3\n42YorpubPPTQQwWOKHd3Tlu+7r7/4ccfZOD8gcIQ7PuF9/24r6xLt24c4xpgHX+69rPb8na3Lru7\nzV8Kuhe2zxcsWCB5eSJvvmnd59y26cqod1ZJtThfYQhydwxysmVTkYMH3eaj1PUODeSqtFwqGFwr\nZrNZZNcuWxSR73avFmKR0H+Hypy55wRE7rwzf/ncld+1pm0bWObuONsUM3eDydwFP8dattlslscf\nf9ypdu5Yk7ZNf1v13Sqp37++MBqp8HgF6TOnj3j18hJ6IF7/8JLmfZrL/mP7nWr7jtdpe+846K6g\nv5GtZcBWJte0BQ0MtKXLyBDp1u1i7bxp901SY3INIRa54wkkp0k9t7unKXW9o5BA7qmTyy9cl1KX\nqXVr+PlnZNkyGu/7J7u27uLjoSvpf1sPzp5NxWKJJjQ0/2GOC7YUxHXBlPDwcHv/9PTp0/H392fw\n4MEATlPSbAur2PJOTEykXbt2REREkJycTFRUFJmZmURERJCYmEhgYKB9IZbtWdsZtGwQB3YewOdX\nH2ZNnkWoVyiHTh7iwy0fsqrCKs6bz1PhSAV6t+7NrJGzqFm1pn1xGbAuDmOxWFizZo29/I796o73\nwHFxG1v5bdPfUlNT8y0045qHxWIhNNTI4sUwejRYLFC7WQYVHuuG5bSZFpmQsroOoctXQ8OGl/Wn\nVao8K2xBGB3spq4L9tHXDz8MgGHJEga2HAhGWLL7fbp0sQDRLF5cwHFupKamOg3AsgVBsAZnWwCb\nN28e8fHxjBs3jiFDhtiDYHBwMOHh4QQFBTkNXBs+fLj9fVRUFOnp6WzcuNE+Uj4qKoqsrCz++eY/\n6fV2Lw7IAdp0asPcV+dy8veThIeHU8u3FqkTUtk2bBsdgztyvtJ5Pt33KTeOuZFn5zzLPvM+kpKS\n7LuhGY1GwsLCMJlMvPzyy4D1YcPdADPb3PLo6Gj7Q4Dr/XK3Cp5t+VqDAfr2he3b4Y474M9t/lT4\n70Ya+DXilxDoEG3m917tYevWQv6i+ekuaEp5ltJu5VBlWKFzknfutDev7/tzpxhiDVJpUiVJWnBE\nQOT22wvOw7Ep2nGwmy29Y7Oz44Ay16Znxx3N3M1Xd/zcca657dgZM2bIrb1vtfeFN+/XXN6a9pY9\nfUpKisTFxdlXfTObzZJiSpHmQ5sL/a3HBLwQIKMn95Pf5vxHzL/9Zm9edxzINmbMmHz3wZbO8TvH\n8rob9Od6/xw/O3ZMpG1b65/kluZZ0mpGG2E0EvIPZEtDf5FNm9z/HYuJrhanPAU6j1xdTwqdjtaw\nIbRsCcePc+MPGdxZ707OnD/DqZsX4+sL338Pe/aQb91yuFi7DA8Pt38/f751hbisrCyioqKIiIhg\n8+bNREREYDQaSUpKcjp9SEiI04pqtqZq2xQ0uLhinK02PHbsWIKCgsjIyKB6zeosO7mMTfU3YcBA\n6w2tef+f7xMSHEJycjIREREEBwfTs2dPe9N3eno64TWbEh/2LDeuqIlxdWWO7j/K1OxFtF89lOjb\nm7Dj+w0ABAYG2qfG9e3bF7DWpG0bpzjWwDMyMuz7nLvOrbdNl3O8DsdrtvH3t2660qoV/L61Jqdm\nr6Zj4y5k+kGnB4/z3YBOsH69/T4UN10tTpUHGsjVdcFx9zFb8zoff8ygVoOs329/n8hIa+B7662L\nzcmu/bu2z2xB0hakbDuMJScnExkZaT9m5syZZGZmOgWziIgI+1aitmZtWwCdPHky06dPB6wBLykp\nifj4eIKDg+nQqwPNnm3G1ylf41fTj6ktppI0JYnQ0FC2bNnCli1bsFgsbNy4EUSYP3Yswd98w+4X\nX+TrBo0JGfEcDXMOc+Db07ydBnV2VuDPRrC1w1mmZkzi1VcG8OijjxIUFITRaGTlypVkZWWRnZ1N\nUFCQfY58eno68fHx5OTkOG3xautXN5lMhIeHEx0dzdKlS+3dBI730PH3v/+28NVX1m1ld6af4MjM\nldxT736O7YBu0X+z4tmu8NVXxMfHX8mfXilVRpV2K4fyZDt22JvX/zqeLX5v+AmxyMyPtwuIhIdf\nTHqppUNtTdeuaW0biTh+FhcX5zSa3dYcb2sCd11G1bF5/d8f/Ftq/auWEIWEDg2VcW+Mc0qftnmz\nxI0aJTJ7tqR06iRSu7akXBgavgBkDMjb1JDuXo0lsVec1A+KE9gv3sF3ifHZykI7hCFIm4k3yMBR\nj8vmzZud5q47dgX06tUr3xx1x41T3DWn2zhOt3Nshk9JSZHMTJHGja1/mog2ufL44ieFIUjF15AP\nW1cQ83vvFfq3UKo8Q5vW1fXOaSBUo0b25nXfbzfwSLNHANjjP5/AQEhPN7F6tcU+Shvcrypmy9O2\n0Yjjym1Go5GYmBh707rFYiEyMpLs7GwA+17jMTExREVFsXv3biIiIpxWVQsJsTaX//ujf/Pishc5\n9PMh2t7ZlsHBg4l7OQ7+/JP0qVOx9O1LVo8e9Hz7bUxDhpC8di38+Sc3Vq7FAvqznH/zgfd4lnZ6\nignrk/n09Gp++WMcffoc4lzWPCyzt/JUYDQ+6yBtxwHm7/2AwR8O5JZOt7By5UpCQkKYN28emzdv\nJisri+eff96+MYvj0q62jVMcWxxsTCYTFovFnsY2qM92b6Kjo6ldG1atgvr1wZS2BdPEoYy6bwy5\nFWBA7/N8OutJWLjwSv8JKFVu6fQzVe4Uac/qyZPh1Vfh8cdZN/EpOr3fiTp+dYjevo/3kirw6qvQ\np4/Jqa/ccUqWY5AH8k3Fsh2TmZnJypUrGTx4MEajkWHDhtG7d2+io6Pt09WGDRvGzJkzgYsPDFlZ\nWRzKOsSKnBUs2rsI9sBtlSKY0eJBvvx0KZEWC9kWC2HARxfO17JqVX4KNdK16ShGfhnCjjN98PI6\nyB13LGX8+Hbk5lqXe922bRt16tQhMjKSLVuCmTQJ/vprI/cEHKN5k1hmdTpHzk4gGFpXbM1LfV6i\nQY0GwMX+bcfrNZlMZGRk2KfJ2dZ/d52ONnbsWOLj4+3X7fqgZPv9jz+gUyfYtw86doQeE/7FuLVj\nABi/BsbHzMbw9NOX8S9CKc+n+5ErJS7N5Lbm9erVJS8nR26ZfosQi8QvSRUQqVEjQQ4cKHzVMtdV\n2VyblB1HpNvSms1m+x7kKSkpkpKS4rTqmm3Ft2+++0aaPdtMiEW8J3rLv1/tLeYLTeVmkASQlMqV\nZeiNN0rKkCGyKXmhdO0yVGrWTBFIEzBLs2YJMnt2in1vctfR8rbFaubPT5EGDRYIdJW6zJKnK/vL\nfU0Q794IPRD6IA9Pflg2bXYeQW7rJnDsLnAcKe9u5zd3i8043ifbd7t3i4SEWHdP69DBLO/+8J54\nxRqEWOS5nsj5p54UOXCg0L+3UuUJhTStV7iGwbc4xcbGxpZ2GZSHCXVc6SUoyNqOu2sXhsOHOX5X\nFKv3rqZm8HkOr3uQrKwc+vVrTZ06cPDgQedjL7BtNGIymQgNDbWnSU5OZvXq1TRs2JCDBw/SqFEj\ngoKC2LBhAyLC7t27SU9Pp0aNGuzevZvhw4djsViYNm0a/fr145fffmHSb5PYdWwXtUNqM63lNIZ9\nsZ0NO3fykdHI2latGJSYSOv33uNYaCg0GcRLb7bjuw29OHXqI2688Tz/93+Vee+93rRp04CpU6fy\n0ksv8dxzz9GtWzcOHTrE559/zrZt2wgLC2Pfvl/p2BGaNHmF1O/PkJ4bygOnTvL27wf5Fdh/A2yr\n8Cv7j//O2nnr8fH2Yc6cObRt25ZPP/2UGjVqULVqVb766iuqVKlC1apVad26NefOnaNRo0bAxRaN\n0NBQ/Pz88v1dTCYTe/bsoXXr1gDUqAH33uvHxx/D9u1+5Fla81Dr83y/az3fNxF27fuJe0fOpEKT\nZliqV8+Xp1LlzYQJEwAmlHY5ilNpPxyp8uDXX0UqVRIB2fvZ+0IsUjmusjw9IktAZNSo/Idcam1x\nd4PWbC/X5VcdN0cZOnSomM1miZ8ZL1WGVxHaIDc9cZP8uP1HiYuLk4TGjWUoSFpCgj3ta68lSFRU\nmkAHgQVSq5ZZqlWrLX/8cfF8cXFx9pqyiHX+99ChQyUlJUUeeughufXWW+35paWlyZo1IoGBCwRS\nJLLSm/Jz4w7ydT2k+kvWwXCNnwqUf/3rNafadmF7the08YrjvXS8d67efTdFata0Np7cf7/Ilzu/\nEb84XyEW6dEfOVGlgsgnn7jNT6nyBK2RK5VfqsnEb15eNPj5ZwLWb+bHB24j48hOQutnsWv5/fzx\nB4waBQaHXilbzc9dDR2gQYMGhIaGsnz5csLDw/Hz8+PEiRMYjUZuuOEGdu3aRbVq1TAajfj5+fHj\njz9SuXJlUlNT2blzJ5UbVCblmxSCA4LpFdCLti3acv78eU6vWkXvnBw+8vcnNCySDz4I5D//qcze\nvafw9m5Gs2apvPZaRVq2bIS3d0VefPFF7r33XqKjo+015aCgIA4ePEitWrWoUaMG/v7+1KhRg549\ne7J9+3Zq1qzJZ59No2bNLQQH38mG33bwbnZ3QiMH8vKfe1gXamZ3ldOsO7qWqKwjVK9Sn+lJSdx8\n881kZWXRoIG1Hz0xMZEDBw5QsWJFQkJCOHHiBHPnziUoKAgR4cSJE2zYsMFe+zaZTBw8eJCOHTs6\n3UuTycS993bkrrtg8WL4+WcwfZPMf/4xkq/NX/KL/ym+vEXo/cYnVGvUHL+2bUvgX4lSZUNhNXJP\n7Ti/8ICilJW7AW62QVWFys21rhP644/sfOYhWtywnDPnz1A79Sv+3NiNNWugc+eLyU0mExs3bqRd\nu3Z89NFHhc5tdiyTbeCbbQEYwGk9dpvUn1Lp8b8eNPJuxPibx9uXaN39zDOwbx8prfvzzY7HOHVq\nBgbD59x3n4nu3TNo0CCI8PBwli5dSmBgIHv27OH48eOMGDGCNWvW2EeLZ2dnExUVxfTp02nZsiVh\nYWH2ueJ79uwhICCAH3/8kRdeGEFCQgbvv78e6E2dOjDlmX3MWv8S3wXnQG1ovx3G+/bkrn/NhJtv\ntl+nzcsvv8yIESOc1nS/1L0qaDDhpk3QrRscPw4DBsCrU3fTa2EPfsv5jXo5sHJhBRrP/AgefLDw\nv7dSHkrXWlflnrtR6pcM4gAVK8L770OlSjSatYTxoY8C8FfzgeB9Kt9sp4iICPr06UNERAR9+/Z1\nXmjmAnfrjLuWz2g0Eh0dbR/dbRutvvVb6/riO9/fScdOHcnMzCQ4OJiVhw+zBvj1p/acOhXMrbdO\nZMECE6+/DkeP7iE4OJg1a9bQrl071q9fz86dO/H392fNmjXk5OQQHBzM5s2bycnJAbCXPSMjw6lc\nf/zxB23btiUlZSWTJ0fxn//05sYbwWwO5omJkUR32Er3nNsI9PVhQ2W4b99K/t21HpZ+/TB99hlG\no9E+HW/+/PmEhITYF4dxx/Ve2RaYARg2bBhgfXi69VZYuRJ8feHDD+HfrzRg/eAN3Gq8lT2BcMeg\n82we+Qh88onb8yhVnmkgV2WSu3nbJaZJEyz/+AcA/5zwFS1qNuNkHQvc/g+WLIFz59wv1RoSEmKf\nRgXOQclx8xDb77aaqeMKaADLli0jIyODxMREHn3kUarvrA794ZOVnxAREUFWVhYf+tXlY+CvCmlM\nmwa9e6+kcWPYuHEjkZGRvP7666xfv56VK1dSp04d5s+fT0BAAFFRUbRr144nnniCyMhI/vjjD9LT\n0wkJCWHixIkAfPPNN4SFhdGzZ09OnDjB0aNHGTx4MHFxcWRnb2bEiN306pVFbu5GXn8dfAzf02ZT\ndzq1jeRML3gxEO7a/BH1Yx4gNSqKKKORuLg4p3tmC8rdunVzule2eei2+2QL+BEREcycOROTyWSf\ns165sokvvoAqVSApCeJersU3j6+mV8NeZFeF7v3zMI3QYK6uPxrIVZlU6HrpJcA4YQK0bYv3fjNT\nfqyDl8ELImeR7ZPGihUX0yUmJuY7NiIiApPJlK/Wbdvty/a7bRlXW/Ox7RpnzpxJUFAQw4cPZ+nS\npTRo1ACWw8ETBwHYsGE30zP/ZDIwdsT9hIVlcfz4cTIyMli0aBHBwcE8//zzvPrqq0RGRhIQEOAU\nKLOysnj44YfJzs4mPj6e3bt3k5mZSb9+/QgKCqJv37488cQTJCUl4efnR0pKCvPmzaNDhw7Uq1eP\nv4EhGcMAACAASURBVP8+yoEDY/n00+H4+WXyxReQ9sPzPBrwGe/0mEGFEC+29YaGdwknd3/Lmi5d\n6LB5M8asLDIzM0lPT2fmzJlYLBa+/vpr+72yBe7k5GT7Eq+O9w6sDz+Oa7Q3bGhh2TKoVAkSE+HV\nsb588vBS+oT14WgV6DYgj59feASWLCmGfxVKeQYN5MrjXc72lQWmdWhiv/uDLxlZ+36oLnDfUwx6\n8hwffLAGwL4aGTjXvF0fPF5++WX79LTMzEz7ym2uHBdWSU5OpkGDBtxU/SboDBvWb8BkMrFvHwyh\nEpFAk9YniI6O5sSJE+Tk5NC+fXsyMjIIDg7GaDSybNkyGjRoQGZmJoGBgQQHB9ub/4OCgkhMTLRf\nw4wZMwgODmb69OmsWLGCp556ihtvvJH27dtz/PhxYmJiyMnJ4fjx46xYsYJff53Miy9upHnzVHJy\nshk6dCuzn3qAsZ0/JqxKGFn14cFesCXai1s2byK1VStWDhwIJ0/a74PtfjkGc8cuENtDjq1mHh4e\nbr9Htnvevbu10u3tDdOnw4AYb96ImMp9je4j50Iw/+WFvvDxx5f896BUeaCj1pXHu5w5xIWmDQ7G\n8vff+K1bR4etx1jQMZBjPjs4fdyXUxlD6dHDgr+/8/GO+VksFvz8/Ow18fbt22OxWGjUqBFt27bF\nYrHYR7Db/Pbbb0yaNImbbrqJ5s2bM23aNELDQvn+0Pfc3up2Xrj/BWrVqshb781gBXmsy/Rm+85N\njBkzhtzcXM6fP8+TTz7JpEmT2Lt3L71792b//v00b96cN954g++//566desSFhaGxWIhMDCQDz/8\nkFWrVhETE8OePXtIT09n27Zt1K5dm86dO7N9+3bOnDnDzp07OXr0KPfffz/VqlUjNDSUTp1upUqV\nDfj7n8ZiqcEff9Rm3VcVaSix3FT9Fw747eS7PCG1ni+djgpD92RyfMMGVp8+zZuzZwNQt25dMjIy\n7JuzuN5P233y8/PDz8/PPhreUaNG0K4dLFsGP/0Ev/wcwEexD7A1+ye2nNjFkibC3fGfUOumptbd\nWJTycIWNWtcauVIOjBMmYGnVCt+9Fmb/1gQsQJdYNm77jJkz0+3pHGuWgL15GKy167CwMGt+Fz6z\n7RrmWIu3pZ0yZQoAjz/+OCNGjKBlg5YAfJ/6PQB792bwrndFvgZ27GjMwYOZgLVvfeXKlYwdO5Y6\nderQrl07e4CMi4vj+eefp0+fPowYMQKAo0ePkpqaSmZmJlOmTGHp0qXs3r0bX19f7rzzTnbv3s3S\npUsZPHiw/ZiAgADg4nry6enpdOjQjhYtjvLWW9l06jSdoKAINq7/mO9mf0aLXz+jVlAdDtQ/yWOP\nQf/I6rQyHyBo/HieuOkmhg8bRkZGBmFhYU4j+l1r6pmZmfkGErq2ppw/n8qGDXDDDbBuHQwcUImP\nHviEng16ctgX7nwsj1+f72edu6ZUOaaBXHmMktiPOp+KFTEmJ0OlStw1M5XHW3SFiqch+k0WLrqL\nM2esyVz31nbcDMSR7b1tn/Lk5GSWLl1q/95We1+5ciVvvvkmISEh1A+sD/5g6G5g8uTJ/8/euQdE\nVad9/AOiyGVGxhEZBgTBcSQRUUQQ8gKoIGkplalUmsZaaeaWa+Vqblu6vl12N3PRStTVDLFMJE0c\nJZnUgAxGLqIIIwjCMDLgIDcRVN4/xjmLdt/ttu97Pv+EM+ccxt+cfM7z/J7n+6WiooJ3O6+iA4yX\nVXR1qTEajcI1jEYjsbGxQgf6hg0bGDt2LG+88QZms1kwYvHx8aGhoYH4+Hi0Wi2LFy8mLi4OiURC\nQ0MDMpkMmUxGamqqMMZmzYat3e4xMTGUlJTg4+NDYKAfEkkxL76YyCOPyLGze4GC9GDqNmUiPRFE\nZ+11kqddYdKL7tT1vI7f1q0wdy4Ro0cLPuXdTWYAobHNZDIRHx//tSbD7usbExODvz8cPgyOjsns\n3w9Ln7bn44f2Eu0bjelWMC9ZMgd270ZE5P8q4hy5yP9r7jT2EHjtNXQvvoj3IHfuWtiJ6Wo97HmT\n1ffP4c9//te8851Y55/vvO6dc9HwrwzTOm9tnTGvrqkmdFEoDAD93/W8supltu/cyfvAXP7B9Oky\nRo+uYP78+ULANZvNNDY24uLiIgTjiIgIVCoVubm5NDU1MWvWLNLT0wW/dKsTm5+fH9nZ2aSkpLBq\n1SrA4q+enZ1NY2Mj2dnZgktbamoqVVVVLF26VAisCoWChQsXEhgYRk1NLMnJJXR2+oHiA3pGbKGz\n7Aq9+vTgr/W2hBV2ktO/P3G7d6M1GPDz80OhUHzjTP2PITsbJk60eJuvWqXkj6uvct+u+8ioyMC9\nGRK3QNw7KTBr1r91fRGRXxtxjlxE5Fu4M4gL5dxlywgKCUF+vpb11cMsr01dw1tJNly+jJARWzPK\nO5ve9Hq98LpOpxNGz7qPpSmVSoqKili3bh0KhYLExERLY1yZHq8oLwiE3NJctm/axAtAV49eQBgt\nLRHU1NSwZs0aVCoVGo2G4uJiMjMzkclk+Pn5ERcXh0ql4ujRo/j4+DBr1ix2795NTU0NYCnLA5w4\ncYIZM2Zw8uRJnnrqKfR6Pa6uruzevVsI4kuWLKGgoICioiIaGxtpbm4G/vVwYjQaWbJkCWvXruQv\nf1FQVRVPdHQJPUzRdO7bA57RdPS6wZJJnTwb3ZuWy3Uop05FfuoUQUFBFBUVCTP11usmJiZiMBiE\n9f2mef3uax8WZqmg9+ihZM0a2PKuA3/2+zORAyOplcBTD4H+6XgMmzb9m3eKiMhvlx8SyJ8EtgGv\nAgOAPwALgL4/4+cSEfnR/JDZ8+87Ruig7tbFPnuDlnv6jAaHRprufoZXX0XInq0PAt0zSZ1OR1hY\nGDqdjtTUVIKCgggICBD2f63ldIPBgF6vF85dvHgxJpMJPz8/hngPgSYoqiiC9nYAIp2cgCCOH7eo\npXl4eBAQEIBarWbs2LEsX74cgCeffBKA5557jqioKADWrVtHVFQUJpOJtLQ0SktLkcvlSCQSnnji\nCZYuXUpFRQWLFy9m3bp1eHl58e677+Lv7y88lOj1emJjY5FIJKSmpmIymVi7dq1Q0rd6kB89msy2\nbRGsXq1nQfwkSFPApSQw9+a4UzvrX3DgL5I2kt58E01MDDHjxwt+5QaDAYVCQVhY2G1rGhERAfC1\n/oLuY39KpY6VKy3f7zPPQE1lOPvn7GeC9wQuKSHy0ZtcfWkxpKR8730iIvLfxA/pWncF3gSqgNeB\nQ0B/LAG9DEs70C+N2LUu8jW+Tf/8hxxjdTC7DVdX6NULm4wMxl24ybsjurjer4CvUsOIn6LC2/vr\nHfCJiYmMHj0atVpNYWEhc+ZYlOL279/PsGHDhC5sjUbDyJEjsbOzo7a2lpaWFtzd3XF0dKSlpQVt\nlhZ9k567A+9mKB7UvvceMokzu3o8z9Wrffj732NQKl3YvHmzILV67NgxFi9ejJeXFzk5OcycOROD\nwcDIkSPx8/MjOTmZefPmMXPmTKqqqti6dSsvvvgi9fX1nD59mtLSUo4cOUJ8fDyXL1+mV69eDB06\nlMbGRiorK5kwYQK7du1Cr9fz/PPP89ZbbxETE4OjoyOurq4MHjyYlpYW6uvreffdd4mNnYC//3lu\n3CiHWlvqvtoII3Np6VvB0V6gvgLBBedp2r2b9PZ2ps6cSVlZGWq1Gnd3d+GzA0IXe3Nzs6DVfv78\nedra2oR9fHd3dyIj3bl2zcCJExLS0iByQi+WT32QjPwMSmwNpPrBjL/sReY9BIYN+xF3l4jIr8t3\nda3/kEA+HDgHXAaGYMnOvwJSgIeAnJ/kU/44xEAu8oP4xgD9DXQ/JjExkRCrAUdoKGg09Ck8x80R\nAWRerqXLsQeGozN46KHbf4dGo2HOnDlIJBJeeOEFQkJCBJOQ8PDw20bVmpqacHd359VXXyUhIUE4\nTqlU0tXVha2XLQdqD+Deyx2POilz0tIokkj4XOaA2dyXmJhBjBnjxs2bN5HL5Rw4cIC7775bsBfd\nv38/DQ0NHD16FLBkr5999hlarRaJRMKlS5d4/PHHOXDgAOfOnaNnz544Ozuj1+uRy+UUFxczc+ZM\njh8/TmBgID169KCkpITBgwczd+5cHn/8cWbPnk1oaCjLly9nxIgRtLW1sWvXLm7cuMEjjzxCYWEh\nQ4YMYfDgASxbFsMgZQmVaQpMRb1g4jlKlCC16UPC6VqcCwqotbNDcffdNDc3U1ZWRktLC4WFhahU\nKmHtrGukUqkEu9S1a9cyfvx4YW0nTpRgNkNWFuzdC9On9eL3U2fz6eefUuZwiT0e8MCbe3HxUsOt\nWX8Rkd86/+n42UHgQWA0sKbb611YsnQRkd8s/45CXHfRl+4l9rgPdKAEVIf4eO9Nvvji9t/R3Z/c\n2rxm3Qe3vp6cnCyUjwGmT58OIHSyW8vuNrWWnpbju49z9PhxkgF69iQyMg6AoiLLOXK5nNzcXDIz\nM2loaKC5uZmgoCDWr1/PqlWr6NOnDz4+PqxZswa1Wo2DgwMRERHMmjWLtLQ0vLy8WLduHYGBgURF\nRQlBvLS0lA0bNlBVVYWfnx81NTVERUUJc+WzZ8+moqKCFStWsGDBAhoaGsjNzSUhIUFYE5VKRUlJ\nibAuLi4N7Ng+ludio3HLeARKYeO0K8ybOpSuq1fhxRfRPvYYylsTAFadduvawTfr18+fP/+278/G\nBv7+d4iO1tHcDLGxYKqRcHzlcUI9QqnxhMi5XVxc9DB8w967iMh/Gz8kkLcDHwLVwD3AVOA+4Bng\nys/30UREfiPcdRe88gr+deDZ0gOcL4FbAcuWQffhCWtgyc7Ovu307vrhVhEU67FW2VaVSoVSqRQC\nl+mcCZrg2uhrNDc3Ew9gb8+AAUbAleTkFYJyW1NTEydPnqSgoACJRMK4cRazFa1WS3t7u/B6aWkp\nvr6+pKamolAo8Pf3JzU1FaPRSEVFBbm5ubftt8vlcpYsWcLu3buZPn06ubm5uLi4MHz4cNLT00lL\nS2PdunWCAlxwcDBJSUn4+PiQmJjI0aNHOXHihPAgY12D6GgVS6b4MXfyn6AUdricYd74Ybja9SDi\nyBE0w4YRJJNhNBqFdTKZTBgMBmbOnAnwNbW3O2fM8/N1fPJJEBMngtEIMTHQfkWK5hGNxWilhyWY\nVy96BG49XP2W6P73ExH5Pv6T8TMXYCTgANzEsnf+SyGOn4n8styyO/2d20mSRoFzzl9oObSClG+Z\naLJaqHYfR3N1dRV02a1ZfHejFes5BoMBd3d3pP8jpaW+hfp7D6KJvAf5kCFceSWZWbMU9OunZedO\nOXq9HplMBlhm2fV6Penp6cTGxhIWFoZCoWDbtm3U1NRQWlqKWq1GIpEglUrJz8/HaDRy/PhxFi1a\nhMlkwtXVldbWVtra2jCbzcTFxVFcXIxEIiEvL48FCxZQUVEBgI+PD8nJyYSFhREbGwtASUmJ8HCw\ne/duioqKLO5t6enU1NQIFQjr567o0caq4sVQ3sGA5rFszC5hmqmeRHt74jZtwhgYiEKhEARp5HK5\nsI53YjAYhA5461RAUxNERFjU34KDITMTrts1MmnHJPLy8hhsD9rtNig3vg8PP/xT3jEiIj8pP9f4\nWSOQiaX0/ksGcRGRX55bJfbYC3YAeI9KBjS8+CKCSEz3rM4qEGMNODExMUIQt5bVu3dcWzXHrQpw\np06dok9hH9DBFxU64oEGGxucnU3AGurrK7C3dyUuLo6KigrMZjMNDQ2EhYXxyiuvEBYWxurVq1Eq\nlcLI2fLly8nKyiIqKor8/HxGjBjBU089xbx58/Dw8MDR0REPDw/Ky8uJiIhgwYIFqFQqqqqqMBqN\nLF++nBMnTpCfn4+Pjw8A/v7+wlw6WMr91rL+ihUrSE5OZv369cC/5Gz1ej1hYWEABLsMYNvkA2Bv\nz8UeJ5gT4EFpZBSqa9dQLlhA0K5daDMy8PPzIyIi4rZxweTk5K9l5tbZeOu6SqUW+1NfX8jNtdiV\nNxrbOPzoYfx9/SmTWzLz2kWPWvxR+XHa/SIivwVEQRgRkR/Bldf+TL/Wl+mygZH7Kskt9OKNNyAg\n4JuFZb5JcCY5OZmKigpWrlx523HdBVE0Gg2L/7aY8+HnednmYS796QM2TpmCYcsW7r9fyZdfTmPd\nuiXk5SUBUFlZSWRkJEajkZiYGFJTUxkxYoQQcNeuXcuECROYPn06ycnJxMTECJ9t+fLlLFq0CBcX\nF1QqlVDuT09PJzMzkwULFgBQUVFBU1MTRqMRtVqNi4sLVVVVFBcX4+XlhclkYsWKFYClFH706FGi\noqLIzc0lODhYyMxdXFxobGykqamJwMBAUlNTGTI2jLWf/hF8ruHcMZbzA6dw6uVVuAIMH87zUikZ\nx48La3NnVv5NHvDd0evh7ruhrg7i4+H998Hc3kDUjigKLxXiZwLtDhvcNu6ARx75UffEv8u3iQrB\nNwsIifz/RhSEERH5D+ie9eUEjCa8UcINWwgPsZSJ16yB4OB/Bevuoi93ZpBgmYm2lqKt13Z1dcVo\nNApNXTExMbg4uIAWzkgvkAjo2toAsExkHUCvB19fX1asWMG+ffuQSqXEx8cjl8tZv3498+fPx2w2\nU1BQwPvvv8/YsWNpaGjAycnptgeM6dOnk5+fT3FxsbAnvnr1aoKDg4mLi0Mul7N161Zqamrw8vKi\nra2NmpoaYfTNOltudVIDS9a9dOlSkpIsDxoNDQ1kZ2fj4+PD4sWLyczMxMvLCz8/P3x9fRnqquD5\niNXYXJPR0nkCt/dfxzt1HwqFgqDCQnYUF5N8S6LXWt2wzp1b17V7dcPKCy+8gMFgQKWyZOa9e+tI\nToY//AH6OsjJeDSDYf2HUeIKsfFdtD7+r8z85+a7VOzEIC7yYxAzchGRH8nBo+9w7+dPcdMWphT+\njkN73+OZZ2DePEvZ3Gg0YjKZvln69Q7u1BK37vPq9XomzZrEiDdG0F7TTtIZMHb4s/L0aTZvhoUL\nkwkNhb17IwSVOetefENDgyDZGhwczJo1lmETX19fFAoFUqmUmpoaPDw8qKmpISsri61btwoZOEBk\nZCTz589nzZo1+Pv7ExYWxvr16wkJCUEmk3HixAn8/f2pqqoSZrzLy8txdHQU/j7r1q0T5GetmThA\nVVUVUVFRNDQ0CPvt1mrAoWNZ/OPaTq43l2PXQ8nTDg8y+vBR4k+fBhsb1k6YwMrPPkOXny8Euzur\nGd+2zkqlkowMuOce6OzU8frrQSxfDnWtdYRvCed85XkevAi794Dthx/Bgw/+mNtCRORnRczIRUR+\nBN+3R3pP1JNs7m3pnj40cDPq4S+xcSNIJJZxs6CgoO8M4t3dvqwd7EVFReh0OoxGI66ulr3vIf2G\n8F78e+AEi8ZDc2MVmk8/xdHRkrVXVlquV1JSgslkYtGiRaSlpbF161YWL15MbGwsycnJ2Nvb89RT\nTxESEkJgYCD5+fl4eHgQHBxMa2sr4eHhJCUlkZaWRn19Pa+//jo1NTVotVr8/f3RarWUlJQI+89P\nP/00paWlpKamEhhocWrz8vIiLi4OJycnnJycbvMY3717Ny4uLkLjXHFxMa6urpw4cYLY2Fjy8/OR\nyWTo9XpUyv4svPkQvRqHc93BwFuZiVx57QV49VXWdnWxUquFWbMwXbwIWErQMTExt5nIfNf3OGkS\n7NgBEMTzz1tK7P2d+rN/zn6krlL2+MOr44Enn4T6+u+8D0REfiuIgVxE5A5+iHHHghd382ZjCEjh\n/Iw1uChX8MILXw8e36QRXlRUJIxkWUvrDQ0NpKenC5rsRqMRg8HAo4GPsnDq7+iQwbuezVQd2Mug\nQQCbMBr9KC+3BDBXV1cSEhKoqqoiLi4O/1se3OvWrWPBggVChu7n58eKFSsoLS3lhRdeEAxLPDw8\n+P3vfy+cc+DAAeGzmc1mkpOTiY2NJT09nWXLlrFgwQLUajUAq1atQqVSkZqaSmlpqfC7V6xYwbp1\n62hubhZm86dPn84rr7yCQqHAw8MDhUJBQkICZrMZmUyGVqtl6CBPPv9DKtLGWdDnBos2P8oqdU/m\nv/8+i3r0wLBnDzGvvMILtzrtrdsRBoOBxMTEr8nwdreYBVCrdbz11q3vcYGl5H6X612kPJCCrY0t\nL0fCHrcGi86rWPkT+S/ghyi7/RYRld1Efl1sbAifvIDOj1I4Jmmgc1g2xZoJjB4cICh/GgwGBg4c\neJuiG1hmxq3KbhqNBk9PT8LDw3F2dqawsJDp06fT1dWF0Whk7969+ODLecNXVN3VTEdtGS88vZ6P\n9sRiMqk5f/5FevZsJScnh3379iGXy5kwYQLBwcG8/fbbPPHEE3zyyScUFhYyaNAgqqurqa6uxsPD\ng7q6OtLT0/H39+fLL7/kscceY8+ePYSGhuLq6kpMTAx5eXkYDAZef/113nzzTRYsWEBVVRWXLl3C\n3t4evV5PYmIiSqWSU6dOMWrUKPr06UN+fj51dXUYjUYCAwPZuXMnGRkZzJw5kyNHjiCTyXBxccHN\nzY2UlBQee+wxwsPDUalU7Ny5E0V/CabP8zA7xdLe9CXHczPI7bzG4wueg1On6CotxUmvJ+Dhh2mx\nt2f9+vXMnTsXT09P1Gr1bY1knZ2dgnKfwWBArVYzZoxl2uDYMYv6W1tbMk/MvB9JLwmHzx/mgBru\n2Xsa9+pGyxC6zX/rLqTI/xX+U4nW3yJiIBf59bG1JWrYfVxKWs/JATexGbqHtL9NISrEHS8vBN3w\nO7F2JFuzXKsdaFBQEJ6enkgkEvbv3090dDR6vZ5hQ4cx2i2M9PMfUVzbQf7+w0waPwuttpmrV4ex\natUwXFwcCQgIoKioiBUrVnDs2DEGDx7MkSNHqKmpobOzk8bGRsLDwykvLycnJ4fr169z7do1Fi5c\nyKFDh8jIyCA8PByz2czx48e5cOECN2/epKqqyjLXLpWSnZ2N2WymvLwcs9mMp6cnPXv2JCUlhUmT\nJgEwcOBACgoKhNG0nJwcZs2axXvvvYe9vT0qlYpBgwaRkpLCmDFjSEtLY+7cucJonoODAwDPPruE\nyEEqDuzv4qpUR6V7GRU9buAxaR7Ol0wMqqhg27591Lu78/SyZWRlZXH27FkCAgKEhydr4NbpdNTW\n1go/u7u7M3EiGAzw5ZeQmxtAeDjMGTuGyiuV5J7PJy0Q7t3xJf3qW2HyZDGYi/yqfFcg/2+9M8Vm\nN5HfDDfiZ/NIx25SAoDWfkg/+pi8I+O55eXxveh0OkpKSoiPjxcatwBBVMXq/Z22di4zzr6PjRO8\nM20LiaumUFioZPLkZCZMqCA4OJiGhgYKCgqEhrbW1lZiYmIEIRWr7/hTTz1FQUEBBw4cYNGiRZw8\neRKFQkFmZib9+/envb2d3r17k5WVhUqlorW1lUWLFgGwceNGhg4dSlxcHGvXrmXatGnC3yUqKgpX\nV1dMJhN6vZ6TJ0+ybt06tm3bJoygJSUlUVRUxO7du5k7dy47duzAaDRSUlJCRUWFILm6Zs0aPDw8\nuHYN9ukGUxSwEHpfQZalZM30ZVT++TVeq6vDEBqK8tgxDPX1P9rP/OZNWLgQtmwBBwc4dAhCw69x\nT/I9HK04irIJPv8nqJ5YAWvXisFc5Ffju5rd/lvvSjGQi/x2yMujIzSYGQ/3IN33BtQoGXgym9zP\nvLilCwMgZJzdx6Ss2fh3dbkLjXGOjjz/SH/euNFJP5ULHz56jqjQjwDIylpMRUWyYPdpVYoDyx53\nd7W3pKQkPDw8iI2NJTs7m7/+9a88/vjj+Pj4sHz5cu666y569+6Nl5eXkNlKpVJKS0sJCQnh5MmT\nxMTEYDabBdU3o9GIk5MTpaWlNDU1ERwcTGlpqTCDHhERgVarpaCgAI1GQ79+/Th9+jTz5s0jMDCQ\ngoICZs2aRVJSEv7+/hQXF5OQkMDu3btpbm4mNHQs69Z/yTnJ+yA3Iw/yZm2/Jxn90l9R1NejHT8e\n+YoVuPbv/4NGt7rPaefm6ti0KYitWy0CMpmZMGRYK/ck38OxymMMuAKfbwOf378Mf/rTj7s3voNv\n0hgQEfk2xEAuIvJzExlJ2xdaJq0aSHbXBahXM+bscbSf9sfe3hKMjUbjt0qL3plJdh+p0mg05Obm\nsnLlSnZMnUKSm4bjJTB0+FCCr/2THf/0wM0tlRdfhPHjw0hPT8fHx0docJs/fz4rVqwQHN0aGxuF\nIK7VaoUgazQa6dOnD/7+/kilUrZv346Liwve3t7Ce3V1dcJnrKio4J577qGgoABA6GB3cnIStNmt\noi9WpTtXV1dWr15NWFgYPj4+gunL/PnzhRn0qKgokpKSWLFiBdnZ2YSFhWEymejqgo8+dWfrV/dB\nYCU9ceTTGa8jj1tG0LVrJMbFsXjv3m9d3zvXuXsgvXED4uIM7N9fhEwWQFaWEk/fFqbsnMIXF7/A\nuxE+3AIhL66FP/7x371LRET+bcTxMxGRn5s//AHHTji4vYOhsuHQr5Qc94nMXXiFri6EsTRrdt29\ns7p7cLG+by2vW0VlVq5cicFgYO57W3jyQxucHOCM0xlsR79H//5aLl0Ko7l5MUFBQYKaW3FxMS4u\nLmzbto34+HhOnjwpzHOXlJQIv9NqvmJvb88rr7yC0WikpqZGCMyOjo4oFAra29sJDg7G29ubyMhI\nXn75ZcrLyxk8eDCenp4sXboUhUJBaWmpEMTz8vIoKChAr9eTm5vL888/L3S1b9q0SRhp27ZtG0aj\nkaVLl6LX6/H19cVkMhEWFkZ2djYxMTGcP69ny4bh/PXhs1A+iU5lGzEZS9n+uygA4vbtw/D++8Ia\nWrvuvymIg0W0xkqPHrBnj5IpU2Iwm5VMngwNtc4cfPggYzzHUOkCc+ZD9Wsr4c03/6NbRUTkp0YM\n5CIiPwWxsXDXXbiUGzja5wkGOKlAdZoPbe/jpVeuArdn3tbM/M5RKes89J1BRzjOw4P4hx5jm+hO\ncgAAIABJREFUfznQAv8sSOKhPzQAJl55Rcfjj79AfHw8ERERTJ8+nbCwMJKTk3F1dUWtViOXy6mq\nquLEiROcPHmSyspKNBoN/v7+1NbWsnr1ahQKhWCS8vvf/57y8nJBtjU3NxewPCRotVrs7e1xdHTk\nypUrrF+/HqlUSlNTE8nJyURFRVFbW0tUVBQqlUoQobEes379ekG7PTY2lnXr1lFUVERVVRVeXl7k\n5uaSnZ2NTCZDp9MRFxdHcnIyzy1x4KMnNbBrMl2XbvB2RzrzEgI52tUFTz2F0mzGYDAID0Pd17O7\nEtzixYtvU+3r1QteeknH2LFQXW2ZOb/aKOXQw4cIVgZT3hci54HhleVwq3ogIvJbQOxaFxG5hcFg\n+NqomBWNRoPqO7rXNIcPoxo2DD75BOfKWuLeOsD7uo+4Kj3N8XMFeLfOZPxYl69dp6urC4lEIrzu\n7u4ufA5r97pcLufIkSPcddddFhW1oCDs/7KR0itQ2gl61ZdMdvsdZwuUmM21jB1rR15eLt7e3qSn\npzN//nzGjRvHli1bWLp0KXZ2dkRHR+Pi4oKDgwN1dXVcuHCB0NBQiouL8fHxISoqik8//ZRevXrh\n7OxMZ2cnUqmUjo4O/P39UalU3Lhxg4EDB1JXV0dVVRVdXV3MnDkTqVRK3759hY7xwsJCDAaDYOzS\n0NCAnZ0dZWVluLq64ujoiJ2dHRcuXMDR0ZHs7GyG3Zrha2xsFAxWcnNzqaioQKVS0bOnHrcenmQf\nknEzrJCCPrXIA3yJP1GHTXo6kiefpPnGDcrKyoQ1Botxi1wuF/5853c6YIA7998PGg2cOaPjyBF3\nHnukN48GzeTw+cOcuWnkUzU8+LdDOLv0h9Gj//0bTkTkR/BdXetiRi4icovv6nj+vqakmJgYiw1m\n//5w6hQDT1Xw8b0f4GjTF4Yc4PFP5pOpvfm161ib3ayvd8/aNRoN8fHxKJVKwa8cgKFDUd57L4v0\ncM94FZfPX6Z82ELk/Tu4cCGON97IJj4+HpPJRE1NDQEBASQmJrJ9+3ZWr17NW2+9hclkQi6XI5VK\nycvLw2w2ExUVhb29PXl5ebi6uuLg4MCBAwcAKC8v5+DBg1y7ZvFHt0q5ZmZm4uvrS3BwMAsWLGDD\nhg0kJyeTkZGBl5cXgYGBgsjN0qVLcXBwwGw2s3HjRsrLy/Hx8REkYq1mKNbO+7CwMEHWVaFQCEYz\nRqOR7Oxs3NzM/GP5TOzfux8u25MkL2fp3P50VVTAAw9QdKuKcef3+n2d7S4ulkCuVgdRUABTp0Kv\nmzKOPHqE4W7DOdcPJs6FuucXwy0t+W/im8SARER+DsRmNxGRn5I1azC89BLK2Fg4eJCTNScZu3ki\nnTYt9C58movvvk2/frf/b/dtLljWZqzu7xsMBrRaLfHe3jB2LO/06c3LC/pwqe4SsaFLSH/Ggd69\no9DrY/Dw+Nc+8RtvvMGCBQvw8/PDZDIREBAgBESZTCaMp6Wnp5Ofn09lZSX9+/fH39+frKwsLl26\nhJubG5cuXaJnz544OTkRGRkJIJTK8/Ly6N27N+3t7ajVanJzc7G3tyc8PJwDBw4QHx8veJgvWbIE\ngA0bNhAbG4tWqxXc2sxmM2DZu7c24snlchoaGtBoNNTU1BAXFydk6m1tCu5ZmErzA89BcQdPXnUg\n4dBVRi1YYAm0t0bG7uwSt3aud19fqyc8QFUVjB0LFy9CdDR88gk0XTcRuT2SYlMxAZfg6Hbot/Gf\nMG/eT3L7iIh8G9/V7CaW1kVEfkr8/ZFs2ABnz8LMmXgMGskYzzHsLEjhuiKbjIwunoiJvO2Ubyrn\nr127Fnt7e+RyuRBkdDodFRUVhIaGIvH3hyNHCNZXMP6B37Gt9StKe+Tg5zwV45nHOH8e0tPnoVQq\niYuL4+LFi8hkMrq6ukhKSsJoNFrEZoYNIzQ0lIMHD1JfX09dXR3Xrl2jo6OD0tJSHBwcyM3Nxd3d\nHScnJ9ra2ujbty9Xr16lrq6OAQMGkJWVRWxsLJMmTcJoNDJ+/HjS0tKYNGkSLi4unD59GpPJRE5O\nDo6OjrzxxhscPHiQjz/+mNjYWBobG3F0dKSyspJp06ZRXV1NXFwcFy5c4NSpU8TGxnLw4EFkMhnT\npk3D2dkZlUqFk5MTQUFBeHlJkPc0k7kzgs7B+8kd2onDjR70T9PhLpXCrYCvUqmEbYvu42fd17/7\nvnqfPpZsfPduKCqC7GwdC+ermOn/AAfKDnDGtp4jvvDQX/bhMHAwDB/+k99OIiJWRGU3EZFfCkdH\ni1zYV19BeztMn86gvj70uxnAwQsfYXTQ0mBw4Z6AMV87NTExkZCQEBYtWsTSpUsJDw8nKysLR0dH\nmpubUavVqFSqf+2ph4ZCSgo2xVXYPrqQLy5mcVX9JT3P38/pL/vx0ktxDB5skSetrq4mNTWVmJgY\n7Ozs6N27N+7u7uzbt49hw4bx/vvv88knn+Dv78/QoUNpbm7G29ubnj17Mm7cOHx8fLC1tSUoKIim\npiaqq6uZMmUK5eXleHl5kZeXx2effYZcLmfXrl10dnYik8lYtGgRZ86cwdvbm4CAAFpbW9m8eTPB\nwcFotVp69+4NWEbXpk2bhslkYs6cOZSVlTFs2DCuX79OV1cXgwcPpr6+ng8++EB4+GhpaRH2v+vr\nzzN5lC/pqZPpdNvDl3fdpN0EOTsPM3n0aLgl2wqWwG3tRSgrKxPkW63r371XQi63NL2lpMDZs+5U\nV8OE8CYeC3mMT859whm7y3zmCw+tSaW3eijc6sgXEfmpEffIRUR+SZ591lLO3bkTamsBWDxxBvex\nBYB/lD3L1rwdt52i0+lQqVRoNBo2btyIUqkkMTGRgIAAtFqtYLJiDUaurq5w773g5wcGA/9jN5zZ\n4bNp7WzB+aHpYJtGQoKG8nIT8+bNw8/PT7AYValUyGQy/Pz8UKvVZGdnI5fL2bRpE1KplMbGRmpq\naoiJiaG8vJzm5mbKy8uJj4+nvLyc0tJSZs6cyc6dOzl+/DgeHh5EREQQFxdHVlaWkIm3tbWRnZ1N\nW1sbISEhJCQkEBISQp8+fUhNTaVXr14AzJo1i4qKCtLT09Hr9SxatAiFQsH69esJCAhg9+7dJCUl\nYTabWbp0KREREaSmplJSUoJWq0Wn0+Hq6kpXVwmblvhgf3QDGGDHTOgIAObMgeJijEaj0JNgLacr\nFArAUlK3Grvcuc0xciR8+qlF+W3rVvjb35QonN05Ou8oXrZe5ClhysNdNM2bDampt537fU56IiI/\nBWJGLiLyE2Nob0dSUQGnT4O9PUycCEBc2AjeXe9Cm1LDgdL9jFAE4tfPDwB3d/fbzFQAPD09USqV\nBAQE0NTUJBipuLu7WwxXDh9m85kzOJ0/j0qvR3PNhyt9m6hu0yN3vYm5YC7nzx9k7dpHABg0aBC7\ndu1i3LhxREdH8+qrr5KVlcWMGTOIiooSyu+NjY3I5XL0ej0PPPAAEomEU6dOkZmZydixY3F1daWj\no4MHHniArq4u/Pz8SE9Pp6amhoSEBDIyMrC3t6euro4RI0aQk5PDuHHj2Lx5M3V1dZjNZnr37k2/\nfv1oaGjA3d2d7du3Yzabsbe3R6vVUlFRQUhICKtXr+bZZ5/F0dGR2NhY1q5dK7ipdXZ20tXVhZOT\nEyaTibi4ON5991Umj1STdTiAm/6fk+MC/W50YH77Y8atWAGOjlj7a6yTAYDQEGgVzbkTLy8YNQo+\n/BC++ALs7GDaZCkPjHiAfSX7KO7VyDGvLh569WPshwfBLY39b5uCEBH5sYgZuYjIf8jatWt/8LFK\npRL+8AfLHzZtgtZWAHr3hl1Lfw+fv8RNbvDQR7PIrMi87dzuym9WIRPr60ajUcggwdIpv/Sddwhw\nc4OiIgZe6+Q53+foYduDBrcPsVOfQadbSXm5Qjjew8MDk8lEcnIyVVVVTJkyhdzcXNatWydcNy0t\nTRCDAUvTmYeHB83NzeTn51NVVUVrayvFxcWMGDGClJQUlixZgqOjoxCka2triYyMJDU1lfDwcDZt\n2sSKFStoa2sDLP7lvr6+xMbGsmnTJoKDgwkLCyM1NZWDBw/S2tqKXC5n1KhRrFu3DrlcjlarJSYm\nhvT0dDQaDdnZ2bi6uqJQKIRGuISEBGbM8OPtxfdhu+eP4AxLxsJxl0tw//3Q0XHbenefI7dWRKx0\nz6YXLVpE//46NmwwYGsLL70E//gHePXxInNeJgOkA8jygqkPXad19v0W0fZvQMzQRX4OxIxcROQH\nMH78+B93woABcPgwlJWBuzvcyvR8faHsSARF5+u5QTYfV3/MZN/J2LTY3Ja9WefK73TxkkgkrF27\nFmdnZ0uGXl+PWqFAc+QIyps3mbNxK+cLz1PQUYBzcCbXTkg4pjWwZk00R49qOHjwIN7e3hQUFDB7\n9myUSiVKpRKpVMqxY8eQy+X07duXiIgItm/fTm5uLrt27UImkyGVSrl+/ToAZ86cwcnJiePHjyOV\nSjl79iwDBgzgww8/JCYmhvr6eiQSCb1796ayshKAd999F5lMxr333kt4eDg+Pj7s3buXLVu2cOrU\nKbKysmhra8PLy0vwY3/ttdeExraysjKOHTsmlMgXL15MYWEhWVlZODg44OjoyKBBg2hpaeHixWxm\nT5xL6k4b6J/NiTBQnaqidv9JukJDUQ8Zgk6nw8nJibfeegt/f39Gjhx5W0Oc1TAGYOrUqbi7uxMc\nLMHDA/bvt/iYDxoEE0JduG/IfXx89mNOOzSTrbzJnNUf0SM0zPKFd0PM0EX+XcRmNxGRXwOZzFKL\nPXcOnn4ag9GIRCJh7N02bH5hCtfc9HT0y+Pw+cMsj1yOna0dYMn+Zs6ceds/+t1/VqlUODs7o1Qq\n6erqonngQLq2bWNQTQ07WlqIm7aAwhuFlCefRRLuwOWTbjQ1eVJdncJ7773Ho48+ikqloqGhgba2\nNrq6uti1axepqanY2dnh5uZGYWEh48aNo6ioiPb2dkaOHImnpyc3b97EbDYL42k+Pj6o1WpkMhkA\nbm5uREVFcejQIQoLC/H29sZsNlNbW4ujoyNSqZTTp0+TkpLC+fPnaWhoYP369YL2ekBAABs3bsTJ\nyQmZTEZpaSmnT59Gp9MxZcoUZsyYwbhx49BoNEIn/d69e5k2bRrLli3D3t6e6urqW8G/jhsGM6fP\nhIH6OAcdIebAeSarhkBYmLBFIZfLcXZ2vk00Zu3atYILmxVrgA8KAmdnOHLEMpIWGAhhI/syTT2N\nj898TJFTC/2bbhC6fg/cfTcMHPgz32gi/x8QA7mIyK+BWg0ffADl5TB8OJLQUMASBORyG/a/eR92\nw/Zhti3FttmWSD/LWNrUqVMtCm63xqSse+bwr5lzq2KZUqmkuaMDNdD8xRdMVCqxeWgWkksSNJ0a\nrtoXQkkbuVl3M2eOG9u2/Y0///nPTJo0CTs7OyZMmMCFCxewtbWltLSU1tZWvL29ycrKQqFQMHLk\nSB544AFcXV05ePAgBQUF+Pr6EhkZiUqlor29nZCQELKzszEYDOzZs4f8/HzKysq4//77uXLlCgCr\nV6+mpKSE9957TzBHGT9+PD179mTFihWUlJTw8ccf8/zzz3P58mWcnJzQ6/XY29tz6NAhfHx8aG5u\n5vr16xw7dgyNRkNeXh7Dhg0jKioKk8lEYGAgjz/+OHZ2dgwaNIjNmzczaJCUhHte5uPPTnBdWoGD\nFAa+cxj30aMxODsL0wDW9bbyTRUYiURCcnIyAQEW7/Lr1+Hzz2HvXku8DvaXo+qrIqU4hVzX3iz+\nsp2eu/fA+PGWTXYRkf8AMZCLiPwa2Npa3DgOHkRTUIBq8WJBnGTkSPgsoweVmUUQmktRYxELRy3E\noacDYAka1nK6NXhYX7fannZ1dZGZmUl4eDgMHcrbf/sbRWfPMvHJJ8kuKkWChKKWIhwnX6Pjy/lU\nlNmzenUQhw+nc+HCBY4fP86xY8cwm800NzfTq1cvZDIZZWVlTJkyhWHDhpGWlsaNGzcwGo10dnZi\nZ2eHXC6npaVFUGLbvXs3M2fOpKOjg40bN2Iymejo6GDIkCFkZGTQ0tLCgQMH8PT05NChQ9jb2xMV\nFcWBAwe4cuUKmZmZ+Pj4YGdnh8FgwN7eno6ODvr06YO9vT1tbW0UFxczcOBAlEol9vb2ODs74+Dg\ngE6nIzMzE29vbyIiInj66aeZMWMGWq2W6OhoDh48yOOPh3J0yxGMg8ooUoH8K5i4dz87gLtCQigr\nK7stI7fyTZK93c1s7rtPQn095OTAxx9bhgjGDR3Cp2Wfou+sQuY/ivATlbBnD0RGgqfnz3zDifxf\nRgzkIiK/Fv7+8M47qKqrYfJkITOzsYGBAw0kb5nFzb4ZtPct5WbXTSYPmiycat2jlcvlt+3XWjvc\n3d3dCQgIQKfTUdvSwqwbN/A8dYq3s7JYlpTEjAkzSN6fzKW2Knr2yOfSqQXk5Gxh165XhOz3/Pnz\n1NfXk5CQwOeffy7sT9+4cYMLFy7w3HPPkZiYSGFhIRUVFYwbN466ujr8/f0ZN24cKSkphIWF0djY\niMlkEjTV6+vrBZtSe3t7PD09GTFiBBqNhqFDh/LFF1/g5uYGwJIlS7C3t6e1tZXY2FgaGhoIDAzk\nxIkTODg4MHXqVK5cuUJpaSlGo5GqqirMZjM+Pj4MGjQIW1tbrl69ip2dHfHx8SxdupRXX32VwsJC\nAgICOHv2LCtfWMyBj/NpaCyn+EpvRhjbmFNdTVl4OKaWFtzc3ISgba2CfNt+tk6nQ61WY2MDU6ZA\naSmcOmWZNJw924YB0gF8UPQBp/p18pTrPdjn5VuC+aRJ8D3ysCIi34bYtS4i8mvh5ASLFll+fv31\n296KilLyjw028IWl1Pz3vW9RdaUKsHTJx8TEoNFoUCqVNDQ0CA5od/4XLF3tyX6WUbbYwkIwGLhk\nvMTB/zlIr/ZedA7Lgv5/oLg4jylT1hIYGEhRURGxsbG0trZiMplISEhALpczf/58IiIi8Lt1vZqa\nGkaNGiV8HqPRSFpaGidPnmTZsmXU1NQI1qRLly5FrVYTGRlJXl4ebW1tVFRU4OrqSn5+PnFxcYSE\nhAgz5JcvX0aj0fDqq6/y0UcfodfrKS0t5cSJEyxZsgQPDw82bdqEk5MTXrcegqZPn05DQwPBwcEU\nFxcD0NTUhKurK1qtloSEBMaNG8fRo0fR6/VERESwfv16lkbfj52vhMvT29nkKoMLFwj68585euQI\nWq0Wg8GARqNBoVAIs+bw9U7z7pMFtrbw979bpgzT0qCkBKaophBwI4D6tno2LAyEBx+EK1csOq+n\nT//bt5KIyLchZuQiIj83/v6WWaXiYnB1FTrYwTKbXHNOia6ylJuDCjCYLzNzWBzOzs5C5g2Wkq51\nr9yqSubs7MyOHTsYMGAA7u7ufJKZychevVCXlsKxYzTfey+9ejjjOcSTQ6cOIRlTS8dXqzlf6kvv\n3md4/vn5vPjii4K2+GuvvUZrayu1tbXk5ORQX1/PP//5TwYOHIiXlxf79u3jL3/5C/7+/gwZMoTC\nwkLy8vK4ceMGUqmUa9eusWbNGsxmM35+fhQWFtLV1UVERAR79+6lqamJiooKysrKuHr1Ko6OjkRE\nRDB06FBqa2uxtbWlvr4eV1dXSktL0el0XL16ldmzZ3P27FnkcjkdHR20tLRga2uLwWDA1dWVyspK\nWlpaOH36tJCpr127FpPJRHt7O4cPH0YqlTLnwTl0NNvwZetxyhwVRF3sQc+yEgZOmsSwBx8EYOTI\nkcK+uUQiITExkYkTJ96mAneng52zs0WPPS/PKuZng9pbzY7CHZwy5vPkGg29z5RCfj6G0lIkc+f+\nUneeyP8hxNK6iMivibOzpaS+b59lvjg4WBAMsbGBmBjYvzmISwM2UtyQz72DZzBqyMjbGt2sPxsM\nBpqbmzEajTg7O3PXXXcJ+7sqlYoiFxccv/qKsrNncT51iiJfX4b0Gcq5Xucoayth+Hg7LmmPo9cH\nMHiwmeZmE/fddx9ubm5cv36dUaNG0dXVRWNjIzk5OTg5OaHVagXL0paWFgBOnjxJQkICR44cYeTI\nkdjb2/PVV18xduxYPv/8c0JDQ6mtrUWtVpOVlYWzszO/+93v0Ol0QlNdfX09I0aM4Ny5c3h6ejJw\n4EC++uorxo0bh1wu5+LFixQXF3Po0CHBICUkJITi4mJMJhNms5kbN24QFRXFsWPHaG1t5ebNm0RF\nRfHMM88wduxY+vbty40bN+jduzfXr18nO/Vzqntf5mr9RcocHuZctY6g0lLUK1dSVl5ObW2tsJ46\nnY7p06cDlt4EqxysdUSte4Ocn5/lWe30aXj8cRg+wIedSTsx9DFg38sR9dTFSLZuRaLXwyOPQN++\nv/RdKPJfjhjIRUR+bQIDoasLtFpLDfaee+CWuIudHdw7WcY72y/Tqcjh8MkKfh/1yG3d6lu3bmX8\n+PFkZWVx9uxZoqOjhVnnkSNHCuVft4EDKRowgHE5OUjOnqXp0iVsJk5idvgctui2UF1yiiED/4Cx\nuA/19Y54eFSQkZGBWq3m9OnTaLVajEYjs2bNwtXVlejoaEwmEyNHjuTMmTOEhYXR3t7OW2+9xeTJ\nk8nJyeHChQvCg8BXX32Fm5sb586do7m5mb59+9LR0UF5eTk6nY4JEyZw6dIlnnzySfLz89Hr9YIj\nm9XpbcCAAbz33ns88cQTKJVKHnnkEfR6PXq9HoPBQK9evVCr1cJ5Xl5etLa24unpyd13380HH3yA\ni4sLBoOBwsJCLly4gIeHB+Xl5cROiaVvl5Qvur6gqkXPXxs86VV/kcKmJsYtWHBbIO/q6rotWN85\nDth9quDaNQOVlRKKiixS+9On2zA6NIht+dvQ1epYFvsSjpUGyM+3fOHfY4srInIn4h65iMhvgZdf\ntmRjra0WW63qauEtDw9IWbwS2qVcsNOwckuG8J7BYCA2NhawqLPJ5XIhcFu7qK3CLkqlkoCYGAzv\nv49BImH30aMEJSXRWG7mjyP+CG5gHPYiNvZfoNVCcXEzY8eOJTs7m9jYWEJCQvD39ycoKIiIiAhM\nJhNjx44lLCwMR0dHKioqkMlkpKamsmrVKoKDgzEajXh4eAjH1NTUIJVKkUgk1NTUcO3aNUaOHImL\niwsZGRn07NmT7Oxshg8fTl1dneBX/vTTTxMWFkZmZiaDBw8mJSUFqVRKQUEBubm5whbA9OnTSUtL\nIywsDA8PD5KTk4WAHhERQVtbGxKJhFmzZpGQkEB8fDxhYWE0NTUB8FDITIb2HQEDmki4y1IZidm3\nD83+/aSnp7NixQphzK+7up7BYLitL8G6nw6g1WpZtcqi3peSYmmC85eMJXpQNM0dzfzpkz/BLetW\ntm4V1P6+je4KcyIi34cYyEVEfilsbCz+2OPGgcGALioKQ2mp8Pa9E/txX98VAKzLfZ5T+TcBKCoq\nEhqsDAYDMTExXzP26B5glEolysmTKfrTnwi0s8Pw3nsoduwg2i2agRcGcsXezJBnLgDR5OYmEBxs\nMTwpKSlh8eLFxMXFkZiYyMKFCwGEpje1Wk1TUxNbt25lw4YNjBs3Tuhez8/PZ/v27UgkEqZPn87r\nr7/O7Nmzkclk+N5SN+vo6GDevHlMmDABf39/YmNj8fDwwGw24+vri4uLC01NTajVahQKBdeuXcPH\nx0c4Nzk5mYKCAo4ePco777xDUlISTU1NtLe3ExERgUwmY9u2bZjNZvLy8lAoFCQlJQFgMpmQSqUA\n5OTk8Jfol8EEZa4ZZDgp0VVVEVNdTU1NDUuXLhXWVKfTodVqSUxMRKlUCt9DYmLibd7m8fHxBAZa\nCi5ubnD0KIwZA78b9CoA28q3Uec3wGKp2thoMdT5DmLEjF3kRyAGchGRXxJ7e4tD1uDBBJWVoXz2\nWYuyyC12LV2K43UPuhSniFmWwuXL3/2PutFoRKPR3NZJrdFoLAF/2TLi9+5F2aMHxrffJvjEF6Ss\nScGx3ZESw0H6jVjCpUuwYYOSoqIiIiIi0Ol0FBUVsXHjRvz9/UlLSwNg3bp1uLi4UFxcTGRkpJAd\nnzx5EoCrV68SGBjIlClT+Pzzz0lPT+fkyZNotVrUajXV1dXMnDmTzMxMqqqqCAwMZPv27cL2wc6d\nO/Hw8MDLy0swQGlsbESj0SCVSgkMDCQ+Pp7BgwcL3evWLFwmk5Genk5BQQEuLi6MGjWK119/nfXr\n1wt73A0NDcTGxhIQEEBcXBx7/7GXyNFRcKWTt8d6YQJ0L7/M2NGjUSgUQtC2ViaszmhgeZj6Jqc0\ng8FAz546Tp60WJOXlsLciXrC+k6jrbON1068Bk8/DYDu9dctWy0iIj8B4h65iMgvjaMjxMai27ED\n99OnoaHBsmduY0PPHj3p0dbFZ7WHaZPqyF4/nbmPyrC99cjdXV0MoKuri5EjRwqXNhgMQue1RCJB\n19qK+5gxdO3bh+TQIeoU3gyf/gAHcg7QM+I813Lu4eQXh8jP38iIEX5cvHgRR0dHgoODiYiIwPGW\nW5hOp+PChQuMHj2ampoaoqOjqayspK6uDl9fX/r374+3tzdpaWm0tbUxYsQICgsLsbOzY8CAAbi5\nueHl5cXNmzcZOnQoL7/8Mvfffz/nzp0jICCA6upqOjo66OrqYtq0aRQUFODp6cmVK1fIz89HJpPR\no0cPzp49S3h4OF1dXaSmpjJw4ECmTZtG661S9ZQpU8jJyWHAgAHs2bOHyspKtm3bRlxcHLt27eLU\nqVOMGTOGYcOG4WbjRpomjeZh1XiUuzOx4RIX+vSh2c2NzZs3YzKZCAgIEFT0rLP8d6rAWbHuq3t6\nSnjkEUvjW3FxANVfNsJdBzllPsWFMw7cd/ES7hcvWlSBblU7RES+D7HZTUTkt0bfvriPG2cpsebk\nQJ8+lrIrYN/Uk89NWTTYlFF1zpuO8jAmTbKcptPpiI6OFi5zZ0Cx/tk6KuXu7g4jRiAyfCH1AAAg\nAElEQVSRSuHwYbqOHWNw+AMcbbtAZV0F/aT5tJ2fBKgYM6aLjAwN8fHxNDc3c/HiReRyOUePHuXl\nl1+mtLQUNzc3hgwZwttvv83s2bO5efMmZ8+exc7OjubmZsrKynj00UfJz89HLpczYsQImpubAfhf\n9t49Lso67+N+g5zPCKMwIIIOCCIhiBgeR1ZFyiI2DaWyVDppLbVW1mrtVlpr3XeJLdamaZqRZIkH\nFFEDUmJQYRQQwQE5KcPAOA7McBSF549xrkCt3ft+7mcfq3m/XryYGa65uLjmevG9ft/D5zNs2DCK\ni4uprq7Gzs4Od3d3LC0tKSkpYezYsVhYWODp6Ul+fj6XLl3CxsaG4OBg+vr6sLe3Bwwr4IyMDPbu\n3cuCBQtQKBQcPnwYR0dHYmNjeeutt1i1ahUvvPCCcEPx7LPPotFoCAsLw8nJSei+z9yTiaWbJZdd\nLlM6xA37mjaea1FzOnIiJefO4ebmhoWFBeHh4WzcuFHwVTeq7t167tPS0gwqe4BGoyQ2Vk99fQEV\n8kVgU8h1nwu0eFzhj5OexOVYvsF1JT4e3N2B25XkbpXnNfH7xtTsZsLE3ciUKbB9u+HxypWG8TRg\nYsREPoxdb3g97G3+vqGV3bsNTwfWym8lLS1NeDww1S6Xy8kODobXXkN84wZmzzzD/rlvYN1qzRXR\nOVzCSmlpkVBQEEhycjIZGRkAgpBLQkICZWVlhIaGEhUVRW1trZB2d3FxQavV4ujoSFlZGfPmzUMm\nk2FnZ4e9vT01NTWA4QajoaEBNzc3mpqaCAoKQq1WCyn58ePHo1Ao+OGHH+ju7qakpAR7e3siIiJo\nbGwkLi4OvV5PQUEBc+fOxc/PD51OR01NDQEBAQQHB1NdXY2rqytqtZqnnnoKb29voqOjKSoqora2\nlpycHPLz8wHw8PBg6tSpbHlzCy42Luin1tPgNZz3mpQElpcTGRlJfHw84eHhyOVyIiIiaG1tFerm\nKpXqts9BKpWiVCqFRrkRI8R8910MmzfDENkeqJ9Go76RP1h9Q9OCWLLb2gy6rlevAtzW9zDwMzRh\n4pcwBXITJv4DDGxGG8TChbBunaFempgIRUUA3Od/H1JfKQxvhal/Z8mSwaJgxn/6A/drrFsP/J2p\nqamEh4cbUvHvvoty0SLE3d2MmL+MdbGGem3H0BSwF7FtmwetrR5kZWWRk5ODi4sL6enptxzuQvz8\n/EhOTqasrIyMjAx6enpwcnJi4cKF1NTU4OPjQ2dnpxCoHR0dyc7OJjQ0lM7OTnp7e+ns7ESr1VJb\nW0tJSQl+fn7cc889jB07loCAAKRSKQ0NDbzxxhvY2NgItfqQkBB0Oh3BwcE4OTlhbW1NcHAw5eXl\nZGRkYGdnR0xMDA0NDfj4+Aj9BREREQAkJSUBht6CjIwMzp48y9iKsQBsG92JHBj7+VdIvL2FYO3h\n4UFMTAyrV68mPDwcDw8PIcgODL7GLvdbSUqC+XFv4XIoExT3UNN2EWlUHRETg6GqCmVcHPT23vn6\n4BeuHRMmbmJKrZsw8R/gF1OkU6capMFOnzb4Yi5YgJmLC8GiYDbLN2PuXcS1U09wNNOZxYsNI06/\ntF9jStbT0xNvb29h3tzOzg6ioyk4eRJJdTUjZdUUzgqkvvkyI+OUaI8/zQ8/fMnf/hbL8uXP4u3t\nTUVFBT/88ANKpZI///nP6HQ6WltbOXjwIMOHD2fp0qWUlJQQEhKCRCIhPDycCxcuUFJSQnt7O5GR\nkYJgS1tbG5cuXSIqKorGxkZcXV0FX/WysjKuX7+Oj48PDQ0NHD9+nOvXrxMaGsrJkydZunQpWq2W\n6upqLl26hFgspqKiQphrz83NJSQkhNLSUnx8fNBoNOTm5nLt2jVsbGyYMWMGx44dIykpiR07dnDu\n3Dk+/vhjjh8/jqeLJ8VHi+maqEfaJaajrokxwwM4oKw1iOyUlXHx4kXs7OxwdHREr9cL2QE7O7tB\nNXOlUolKpcLT03NQanz+/Nk8HGfNoY2PoHXPRFNbQeZMTx6vuIF7eSVotYY+iV+4dkyp9t83phq5\nCRN3M2Zmhn/iBQVQVmYwun70UbxEo6i8Usm5KyUMFWtpzHmIrKw0nnkmhHffXSdYba5b99Njo2Oa\nsd5qbI6bNGmSwfK0o4OWUaPQVVfTUVVNbMsQvpb20XLtHC7WfjSX3I+ZWQW+vr0EBATg4OBAc3Mz\ngYGBKJVKQkND+cc//sHq1avJzs7m0qVLLF68mP7+fvbu3UtZWRkXLlzAyckJDw8PRo4ciVgsJjQ0\nFJVKRXh4OE5OTvj5+ZGTk4NYLKb35mq0qakJe3t7NBoNI0aMYMKECXzzzTfMnz+f/Px8+voM43i2\ntrb09PRQWFiIg4MDCoWC+fPnc/78ecRiMTt37iQ4OBixWMyECRO4evUqO3bs4O2332bjxo3MnDkT\nf39/cnNzUalULFu6DDdvN45sPUKJ7zXeqruBx6kKgj7+kBathtGjRw9qIDxw4ACTJ09GIpFQUFBA\nQUEBkTdldx0dHfH09CQ1NVXomDfi5gaPL7Ijf0s8l0bsRW1ZycEJATx5SoPlj4Xg4YHc3FxQkLuV\nW4O4KbD/vvilQG72nz2U/zP6+02jGyZ+a7S2wuTJUFFhcMo6dIiL+gaCUoO43ncdx6/Ooqu6h7//\nHVatuv3txtqsEaPNqHGcCgz//MPDw0GnM1hryuU8EzaUz+KuYj/EmY73vsbqujn//Cc8+WSMMLtt\nHPPSarWUl5fj6OiIj48PEomEopvlAKN5SmtrK42NjWzatEkQNomJiWHevHnY2tqiUql47rnneP+m\niYy3tzdRUVHIZDLa2tqoqalBJBKxfv16qqurAdi8eTP+/v6oVCo8PDwoLi5m2bJlwu/My8sDDHXq\nU6dOERAQQGxsLOnp6axfv55p06axcOFCVqxYQWRkJDNnzmT9+vUsX74cLy8v5s6dy1MHnuJM0xmm\nFDix6JyOtvHLmPu5wfBGrVaTlpaGh4cH69evF2rjd0qlG89zZWXloHKH8T0ikZgFSYXsc38YnJQE\nVvlTsqsKK4bAkSMQHf2/unxM/LYxM1gg3zFmmwK5CRN3E3V1MGkStLQYRLs3byb58Its3LuRiKBY\nil46hKWlIQsfGvrLuxKCNj+lfI1KZGKxmOxdu+CllxinUrFooTMnxG241E+g9buXmD37UZ54Io1H\nH00kOzubkJAQysrKhBuDsrIy1q5dy5o1a6iurqa1tRUXFxckEokwGpeSkkJoaCharZZdu3YxatQo\nAm5qzOt0OpycnNi9ezcxMTEUFBTg7OyMj48P+/btIygoiKamJsaOHSscd1dXl6C5fvjwYUJCQujo\n6ECj0dDS0kJQUBD29vYcPnyYTz75hFWrVmFlZSUYuqSkpAh/v/H4EhISAEMdvERVwn1f3YcFQ9j8\n6Q0udlpSMXsBM+Mms2LFClJTU4mPjxeCd2pq6qD5ckA4V8ZzfOvNlfF5fz/85cMK/l4aBaPa8M0S\nUX1KTbOTM+KiIhhgymLCBPxyIDel1k2YuJtwcYEZMwxjaadPg60t3lMT2KncSV1nOTHjQ1EUBJGf\nD0uXwvffG5y40tLScHNzE0aj9Hq9oBkOoNfraW9vp729nYCAANLS0ohftAi7yZNpzshgbkUrX3kN\nQa9rxAIzqoseYdo0N9raCqiurub69euIRCJkMhlHjhzBz88PsVjM1atXOXXqFKWlpQQFBXHixAk0\nGg2ffvopI0eOpLW1lZaWFlpaWnByckKhUDB9+nSam5vp6ekRXMSmTJlCY2OjcKxDhw5FoVAwduxY\ntFotTU1NDB8+nJMnT1JXV8eoUaNwc3NjypQpODg4oNVqSUpKQqlUYmtrS2trKz09PURGRqLVaoXV\n/+rVq1EoFDQ1NfGXv/yF/v5+du/ezRdffMGEwAloujQo9ArUzsMIUujpr1Hzpy07yDjwDba2tkye\nPFkoW2i12kEuaAB2dnaoVCrhhsVYT79Vr93MDIbaXGKs+xMcbtxFa6CWSqdRLC1VGUorjz8+uBnC\nxO8eU43chIlfE15eEBQEu3fDsWMMnyrF6p4wjtQcQemwH4+uaKrlJ+juDmH58p9sTgcGC+OXEWNg\nNwaYkJAQsrOzGT5mDA7TplGbthuJvpecbuhfWAnNIRQe8CYhoZ/p0ycSFhZGf38/zc3NdHV1ERMT\nI0i6Hj16lI8++ojm5mb27NnD+PHjMTc3Z/jw4RQWFmJhYUFcXBxJSUmUlJSg1WoBKC4uJjAwEGtr\na7KysmhpaeHatWt4eXnh7OxMZ2cno0ePJjo6mpMnTzJ79mxiY2OxsrKitLSUo0eP0tTURG9vLykp\nKbS0tFBbW4tWqyU0NFRoqBs2bBh6vZ7s7GwaGxuJjY0lLCyMPXv2CA11SqUSJycngkXB7G/cz2W3\nTp44P4y+nmbUuy9TKmpn4cKFVFVVUVtbi52d3SAhHrlczp49e/jDH/4wqG596+cwkNzcXJ5aOAc/\n82nsrd1BuUcrEYrRBNQZLE/T+vsJ+VdpFxO/G+6mQD4XyASSATvgx5/ZbiLQAJwDKu7wc1MgN/Hb\nZuxYsLeHo0dRHjzInFc/5vKQDk4pT0FQBr3lqyk4epTr15VERxuCuXGleCexklsDilwup7Ozk7Cw\nMKp0OjLVat4+WUWHTx8F/oD+W3raH6C6OIr6+rUMG+ZGe3s7VVVVLFq0CJVKhY2NDdnZ2XR3d9PU\n1ER3d7eQYp8yZQqLFi3i+vXr5Ofno1QquXTpEgkJCZSXlwNQV1dHe3s7UVFRmJub89prr3H+/HlG\njBjBsmXLBDOVuro62traaGpqwsXFhYqKCh5//HG6u7upra3F39+fixcvYm1tjUwm4/XXX+fcuXME\nBgZy+aZ+uouLC6GhoVRUVODt7c2IESOwsbGhurqaiRMn0tTURFhYGBcrLnLuyDlae1rRBIzjWnkj\nUW1n8Ql5jPBFM/H09OTixYv09/cPakrLzc0lNjb2tvNvbEiTy+XC9sbXQkJCUCqVTLsnmLorKkqu\nnGavUyjPlrdjV1VKiK+vySXNhMDd0uw2BLgAzAIagdPAIm4P1EOAo0AnsA347g77MtXITfwmGVjX\npr8fEhKQ795NeHQ0148cJv6bP5KpyMTFbASt/yXD9roXJ07AhAl33t+dmrIG1m3T0tKQSqWIxWLS\nnn+eGampzPOFs38ErjnCl+uZGvIcWVmg0xnq7Gq1WqiVq1QqofackJBAeHg42dnZaDQaSkpKSEhI\nEIxLvLy8iIiIQKPRsHXrViE7AAZHs5ycHIqLi7G5mVL28fGhoKAAf39/6uvruXbtGlZWVnz66aek\npKQI7y0pKQHgqaeeIi8vj5KSEiwtLVm+fDmnTp3C3t4etVqNnZ2d4GceHBzMqVOnSExMpKioCD8/\nP9zc3AgJCaHuRh1TFk/B0tGSxMuz+OJMFv+NFd0vLmf1Rx+RnZ0tWK4az+3AcyqXywc1GN5aJ78T\nLR0tSDZK0F/TM277h5ypX4VFX6/BZGfZsn912Zj4HfBLNfL/pCBMJFAN1AG9wC4g7g7bvQB8C6j/\nY0dmwsRdwiA1LzMzSE0l3N0dcnKw2LKV9PnpRHlH0dp/CZcX5tLVr+XBB+Fmefk2bhUpyc7OHhRg\namtrKSsrAyDxH/+g+eWX+awOos8BVnqIe5P8wseJisqms9NwfDk5OVRWViIWi8nKyhIayIyd3Tk5\nOYAhEGdlZeHl5YVarWb37t288cYb1NbWMmHCBJKSkujo6KCjo4OioiLKy8u5cuUKtra2BAcHExwc\njEqlYvz48QwbNgxvb28iIiJYunQpjY2NxMTE0NjYiE6nw9/fn82bN6NSqbC0tCQiIoLNmzcLqm9d\nXV1ERkayefNmpk6dikQi4b333qOoqIjY2FjBKjUlJQUbtQ3+Tv70+vdS/qCGh/BnJtd44UAedHcj\nEomQy+WDzu1Au9Pw8HDh+apVq+4o3mM8/8bXLl+4zOtTDc5352K28wypho2eew5OnPifX0gmflf8\nJ1Pr9wIi4MDN575AEJA1YBsv4C8YgnkchhW8KbVu4veLvT34+sK330JeHpaPP8lDk57kgOIAl3vO\n4zSugCu5C8n93pLHHgMrq5/flVKppL+/H09PT2GVOH36dKFhKzU1lbjVqzG7coWkb0+T5Q5N3p2Y\nuWtoOb0c2Yk22tv3IJH4EhgYSG5uLq2trQwfPhxnZ2f6+/txc3PDz8+Pt956i4SEBJRKJUuWLKG7\nu5vnn3+eo0ePYmtri7W1NYWFhYSFhWFvb49MJhN80HU6HVlZWTg7O1NRUcHFixcRi8VYWloCMH78\neH788UdycnLw9PREKpWi1WqZOHEiOp0OsVhMdXU1K1euxNXVleLiYlauXMkrr7yCn58ffX19+Pn5\nsWvXLuRyOTY2Njg7O7Ny5UoUCgU2NjbY9tpSLC+mwaceC6KYW3cNe+0FHK9cwfOppygtLcXOzo6N\nGzcikUg4cOAANjY2t9XHZ8+ejVKppKqqivDwcKER0VjqMH4WtbW1BDgEcLTlKLouBWc6/0iozSiC\nrv4IBw7AggXg6vovLxfTbPlvl7ulRh4ESPgpkN8DeDM4kG8F3gYuA/GAgp8J5AB5eXnC/Kivr+//\n/RGbMHE3MHYsnDuHvKQEz/Jy7JY8zQNjHmR3+W6umJ/D3vc8DYfnU1FhzoIFhoW8EaVSyY4dO4iM\njGTjxo0kJCQgl8tpb28XgogxsHh7e6PX6xE/8ggWtfUk7DvLodAhNIvaMI/MpFEeQ5dyGuvWTaai\nolSQQ71+/TpDhw5l5MiRlJaWcuLECVpbW3n44Yeprq7GwsKC/v5+Tp8+Ldw06PV64uLi6O/vp7y8\nnGvXrvHwww9z+vRpLly4wNNPP013dzejR4+mvr6ekSNHMmLECNrb2+nv7ycuLg4LCwuqqqpoa2tD\noVAQExNDZGQklZWVLFmyBK1Wi0KhYP/+/Vy8eBFnZ2dKS0t57LHHeOutt7h06RKzZs2iu7sbT09P\nent7sbGxISYmhpMFJ7HqtUJRr6D1Rh3F7Rt5vuMgFsUnUQ4bxvAZMxCLxUgkEsRiMSEhIUIANbrT\nGb9XVVVRWVlJSEiI4fwOyIgMFJcZ4TUCkb2IjNoMzLxPk569hhXhKuwvlpKano7FpEl4jhz5i5eK\nKYj/dsjLy+OLL74Q4twPP/wAd0Egd8awyt558/n9QBuDG97WAwuAF4EIYA6GYH7hln39LS8vD6lU\nilQqNQVxE79tzMxgxgw8t20zCK57e+M8eSZzRs/h63Nfo7c/i9XQZsoz7ufaNTPBKc246jaqjhnV\n3wRXNBAkRwsKCggLCzM0aZmZoQwLo1deiv3eGq6EWnHZVQujdtBQepqj344h7gFnpNJp7Nixg6tX\nrzJmzBjS09O5fPkycXFxKBQKoSPdOMPu4uKCjY0NZ86coaamhsuXL6NSqUhKShKU23Jzc9HpdMyZ\nM4euri70ej319fW0tbXR2dlJfHw8DQ0NbNu2DT8/Pzw8PPD09OTq1asUFBQwffp08vLyuHr1Kl5e\nXvj6+grbXb58GV9fXzQaDYsWLaKpqYklS5bg4uJCV1eXwdp0+HA2btxIREQEozxGUVJawhXbK5gF\nNlBT9joTOEjZ998TtnQpuLsLzWvGRjalUik4oPX29grn2jgaaHSI8/T0FLbX6XTC5zFu2DgOKg6i\nvKaAG6M4qHyM5R6FRNbX4XnlCjzyCIKnrYnfNL6+vkKMk0qld82KXAX8FdiPoZEtBXgXuDJgm5QB\nXwHAh8DeO+zLlFo38fvCwQFGjIDvvoMffiDb25vJk2cjahOR3ZzNtWEnMcOc/J0z8PWF8eNvtzj9\nOTZu3EhoaCj9/f3o9Xo2btyIp5cXDvPnE5SXz7T9jbg6uFNwowvG19M4/AQlmffi6VCHSDSUMWPG\noFarefbZZzl+/DgymYwRI0Zw48YNvL29GTNmDHK5nL179zJz5kzi4+NxcXHhxo0bNDY20t7eTkVF\nBRcuXCAgIIDt27eTm5tLY2MjP/zwA6tXr6apqQlLS0uys7MZM2YMSqVSsEA1zqabm5vz/fffExAQ\nQE1NDZ2dnbi5uXHx4kUyMzNJTEzk6NGjPP/88xQWFiKVStm8eTMZGRnY2tpy7NgxLl68KIjVuLu7\nEzUuiiNXj6DxrqNEOQa1ppvEG5fRHzvGRrUaB2dnwsPDhXNdUFDA5s2bmT17tnA+B04MGNPpRuzs\n7AgICGDVqlXMnj0bMzMzAtwC2F6yHZwLURe8zein5hNa9hWUlEB3N8ye/X9+eZm4+7lbbEyvA88D\n2cB5IB1D2vyZm18mTJj4JRYuhIceAp2OmA8+AI2GZfcvY9f8XZibmdMv/StM+Iynn4bjxw1v+SXn\nLKVSSVpaGjqdTuhAz8vLIyIigqysLFQ6HWWvvYbX6NGsz7yC/FIA4jYv6KmiSPIQf/rmAJFRUmQy\nGTExMSxfvpzk5GQSExPZvHkz8fHxxMTEoFarCQ0NJS4uDq1Wi4eHBxKJBL1ej1arJSIiAldXV557\n7jk8PDyEjnTj+FltbS3jx49HJBJhbW1NcXExOp0OgPj4eCZMmIBCoaClpYW4uDihiz0gIECwZJ0x\nYwabNm3i1VdfRSQSUVxcTH5+PlKplE8//ZTdu3eTlJTE6tWriY6OZsOGDYSEhDDUbihPBz4NSjCT\nfka6fQqlNj6oKiuJaG5GJpMJ5xJAJBIRHR0tNMPl5eUJn8GqO+jqGpvi1q9fL7wm9ZXy4JgHYWgX\nzHyTF/8hQbf1W7CwgPffhx9/bmrXxO8Vk0SrCRO/JtRqmD4dKisNM2fffw/Ozvyz6J88e/BZzPrN\n6U//jqEtD3Hy5L9W+hw47iaXy1Gr1YL157p162hsbCRp3jzCX3wRqqoo9B3Blr/M4/PL/4T2Pqz1\ngWyZn0L96dPExsYK42cAGo0GNzc39u3bh0KhYOnSpeTn5xMXF0dRURE6nQ69Xg8YJFfHjh2Lj4+P\noJ1u9DRXKBTMnDmTs2fP0tXVRVtbGz09PcycOZOamhqKi4txcnJCp9Nha2vL0KFDmTt3Lrm5uQQE\nBNDR0UFycjKvvvoqAO+//z5qtVo4PuP4WW1tLREREYJ2vE6nIzo6mn379lE/tZ5DxYfg/HTGHvYg\nkW9YPWECFBXdUQrXiLHBTSwW31HSNS0tjcDAwNu8x4+fO070nmhu9PXDJyX8aeE4UpzegLVrYeJE\nKCw0pdh/Z9wt42cmTJj4f0nqN9/AsWMwahQUFxtc09rbeSbiGf4646/0m/Vh/sgirlqcY+5cJTdF\n1AaRlpYmPPbw8Bg0NhUSEkJqqmH0SafTsWnTJsLvuw95airKoCB86i6xZe1BHqmcj0W7Lz2dlTye\nP4/zjjq+3vU1crmcmJgYioqKKCkpYd++fcTFxfHKK68ACI5gq1evBqChoQGAuXPnkpiYyKZNm26T\nPV26dCmHDx8mLy8PNzc35s6dy4svvggYVsBr167F398fd3d3urq68PDwoLGxERsbG4KDgykqKuLV\nV18VzFSMc/CJiYlUV1ejUCgAWLJkCdXV1YL6W0JCAhqNhjVr1vDWhLewu2YHtsepColl5hA75MXF\nyL/7TgjCaWlpqFQqKisrCQ8PJzw8nLS0NKG5zagTP5DExMRB+u/Gm6Dp46bzbMSzYNYHc14hNRUq\n41aBp6dBuverr/7ta8bEbx/TityEiV8jdXWGlfmlSwa3rMxM+m1seHLfk+zI2oG95XQ6UvOYNcuM\nQ4fg5uTWbRiDONzu5HWbkIlWi3LWLFRyOR7u7rD7AJO+3sllcSoUgu+0SFYMXcDLz74MGMbZ8vLy\nSElJoaysjA8++ICZM2fi4uICGAJbeno6Tk5OACgUCiGohYaGsmbNGsaOHUtwcDB6vZ6kpCQh7W5c\nqcfHx9Pa2kpubi42NjacP38eCwsLhg8fzuTJk6mpqaG+vh4nJyeWLl1KdnY2RUVFrF69moyMDMaP\nHw8gHFNraysKhYL33nuPsrIyYdW+ZcsWdHY6jtw4AkOcmJvmw7rr52DJEjzWrr1NYCcvL4/AwECh\nZDEw63Hr6tuIUWjGiLpDjeRjCboeHXyZzX1j5nDwke3w5JMgFoNCYRhPNPG7wLQiN2Hit4avL/KN\nG8HDA3JyYP58zHp72RCzAZFEREfvcRyn7uTYsVW88IJBJO5OpKSkDBI2SU1NRalUolQqKSsrGxTo\ncXVF/MMPyPz92XblCqoHZvPucHfuOb4cgrypO3qK11RvECINJetwFg0NDbz++uukpKTwwQcfMGHC\nBPz8/MjIyKC1tRWZTEZ0dDQREREsWbKEzs5OoqOjCQ0NJTs7m7Vr19LS0kJNTQ3BwcEkJyfj4eGB\nTCbDy8tLaIwzHJorUVFRLFu2jFmzZjFq1CjKy8sZP3481tbWxMfHs2HDBjw8PARrUalUikKhoLGx\nkYyMDCQSCbGxsdTU1KBSqQQjmpCQEFJSUjj8xWEmBU4CvY6TsfaEA+E5OYg9PIQ6eGBgINu2bUMq\nlQoB2+Pmz9PS0gYF9IHfwWD1anyuVCoR2Yv4y9S/AGA+92UOZd3gsOhxQ0lFqTTUy02YwGSaYsLE\nXcGd9NH/FZ6BgRAbC+npUFoKFRXYJjzKMEcP9ir3Yh/4I32n0zlVYIOrK9x770/vNQqHGAVLjL87\nMjJS6LKWSCQ4OjqSnZ39U7rbyorIp55CUlREe0UF95w+xaufvENX03x+PH2W/nGXafFrpo5GHr13\nIefk52hra+Pee+/F2dkZb29venp6qKiowNfXV+guP3LkCM8++yylpaVkZGQglUrp7u6mpKQEa2tr\nFi9ezNmzZ1EqlQQEBBATE0N7ezt1dXWo1WqUSiVNTU20tbVRVFREf38/06ZNQ6fT8fLLL7Nnzx4e\ne+wxPv30U+Lj40lMTGTJkiVIpVIAzM3NOXnyJAsWLGDBggXCvHp/fz82NjYEBNgYJVoAACAASURB\nVATQ1NSEe487GWkZdIc0MrzLjavVTUj+8AdK29qEBryEhIRB3eobN27ExcUFpVKJt7f3oM5143fj\nZ1BaWiqcdwAxYtKPp9M+tAbaRiI/FM4zKWMx374NTp2CxYvB2fl/e9mZ+BVxt3StmzBh4mf4V1rc\nP0twMBw5Yvhn/t13sGQJi0MeY6rPVLTXWpC+vQaAP/8ZduwwrK6VSuWg9K5YLB5UN78Vo782GFbs\n2NjAZ5/h8fDDqLq64L77WD+hla2vfI7jvs+hfRg/fpfHw/+Yj02UDQUFBcKKWSQSUVBQQEpKCuXl\n5axevRqJRIJKpRI6wBMTE8nLy6O1tZW9e/eSmJiITCajvr6eF154gZiYGNLS0khLS2Pu3LmcOXMG\nMNTbjUF6wk3xeb1eT0pKCpGRkWRkZDDr5pD9ggULmDFjBkuWLCE0NJSSkhJGjRol+KzLZDIaGhoI\nDAxErVaTmpqKWCxmSPcQxvuMBwdYOaODGktg505CQkLw8PCgsrKSBQsWCLK3crmc1atXExISwooV\nKwaJwQxcjRtfH3iuAUb5jOLDJz+EEhgyew0VF9v5Z/lUlA88AF1d8Prrd/zMfunzNPHbw7QiN2Hi\n146np8HDfNcuKC7GrKmJKosxyPoLqek5zVPSByjK9eTYMUceeADs7H7yxzaqj90aQAayaNEiwBBk\njOIyjs7OOM6fT1NlJU2lpfR/8w0O4V68+v6LZK+fi9q6khsR1ez/bD/+j/iTOC0RdaMa+5s13bCw\nMAICAti6dStisZiamhqsrKwYN24cXV1dBAUFkZeXh0qlwtXVFW9vb3x8fPjoo48YPnw4o0ePpqOj\nAw8PDx555BHGjBnDvffey+HDh7Gzs6OmpgY7Ozuqq6sB+PLLLwkKCsLNzY2cnBw0Gg09PT2UlJRQ\nXFzMxIkTqampITw8nMDAQPr7+/Hw8OCrr75CrVbj6+vL/v37kUgkJD+TzNZ1O2gX6+l1hPr95zhr\na8v9Dz5Ib28vCxYsoKWlBTs7O0FBb6AQDMCOHTuIi4u7LRMz0LvciOt1V/LJ53L3BbhuTWG6lPCn\nrxH0fRacOQNz54K396D3/NLnaeLXiWlFbsLEr5RfmgMfRFQUZGYaVsubN/NeSzfJk/5EX38fZ8XP\nERd3mfZ2mD1bzpAhP63+jfXigQysi8vlckFMZeDxKJVKMDfH48MPYelSxH19qN98E/Md77Js0XEe\ncvgStr0Kk1z4PvN7Jr8ymf1n9lNZWYmLi8ugEa2QkBC8vLyEx2lpaSQmJgpp79raWjQaDRkZGVhb\nW+Pn5yd0gLu4uAid3tu3b0ckEpGcnIydnR25ubnY2tqi1Wp54YUXCAgIoLy8nLfffps1a9bQ3d2N\no6MjIpFIGIPbt2+fMH5WUlJCYmIioaGh5OfnA/Dxxx+z/Yvt7PhoK5Sac8QT9gy5RmNhIXK5XMgq\nGJvWjONnxsdGJBLJ4P6Dm9wpO+Lt5c1/z/lvAMynv8/VXiUnqp6AlSsNG7z44s83QZj4XWBakZsw\ncRfzP9LO9vWFiAj45hsoKGCyzxS2u9RTqankhScDuVo+gQsXPMnPh0cfvXMne3Z2NmFhYcJKccOG\nDcyePVto/DKuMI3yopiZ4RAdjd7WlrATJyjIySHY34/tJX8naf7HnEiZBr15XG/XctrhNDUXa/Af\n6o+iQoGLiwsxMTEkJydTW1vL008/zZ///GeioqL4/PPPOXbsGI899hhbt27F3d2d6Oho3N3dcXV1\nZe/evTQ2NhIUFMTOnTuxsrLC3NychoYGlEolDg4OuLu7U1FRQU9PD+bm5mg0Guzs7Dh06BBDhgzB\nzc0NvV6PQqHgo48+QqVSUV5ejrm5OT4+PkilUo4fP86KFSs4ePAgTk5OyOVyXnrpJZS1Snqwp+py\nCXoxPK9zZVzSUzQ3NwvmKQUFBeh0OhwcHITU+bp16wSjmls94o24ublx4MAB9u/fL8jqjnQZSWlz\nKRV1ZeDcRtFXD7LwvyNx278NLlyAgAAwrcJ/09wtEq3/l5gCuQkTd0IiMfxD//ZbrI//yIip9/Ft\nfzmFygL2/nUZmRl2lJcbeuNGjpQzYsTgGwU7O7tBAWb2TTnQkJCQ2+RFDxw4gF6vJywsjILeXiTT\npiE5eJCmU6d464knCHx+EmplFhU/TqTPXIRZaA2q5svIkTMrYhZtDW0UFhby+uuvc/36dTo6OgRv\n9H379vHCCy+QlpbGsGHDGD16NGFhYfj7+9Pf349cLic1NZWgoCBOnTrF+PHjiY+PJzg4GGtra/bu\n3YulpSX19fV88MEH9PT0cOnSJV5++WW6u7txcXHB2dmZyZMnc+XKFXbu3Mn06dPx9vbGysoKiUTC\n119/jY+PD97e3pw5c4aenh6WLVtGZmYmwcHB3Bcl5ctdB+jqaUdjqWTKPfdzpb0dd3d3cnNzmTRp\nEu3t7Tg4OAipdaMj3G1NhDdZt24d999/P25ubtx///3AT42JXnjxZd2X9A2X03c+nlqFD9JHzXA8\ncsTQ+Pbss2Tn5Ny2zzv9HhO/PkyB3ISJ3xOBgeDvD3v2MDb3HD/+IYDya5c5eTGHz16dT8ZuW0pL\n4cIFTx58EFpbf6rTGmu0A2u3qampQm3caMnp6elJSEgIp06dws3NzWCPOm8e2V1d2MtkeObns6Ow\nkBc+eYelSfPISp+MVvYguJyg26uR7EvZODg58FLCS+Qfz8fb2xs7OztEIhGZmZmMGDGC5uZmPvvs\nMyZNmkRhYSH+/v5UVlbS1dXFkCFD+OKLL1AoFMyePZvy8nICAwP58MMPmTZtGsOHDycwMBBzc3Nq\namrQ6/V0dnZiYWGBp6cnKpWK7u5uIb0tkUhobW2lu7ubJUuWsHnzZjo6OvDy8iIoKIhNmzaxfv16\nCgoK8PX15ejRo9jb22PXP5Kz3cepa4b+4lrmPvoYarWaSZMmAfD5559z781xgYCAgEHn2KjrPtA1\nbcWKFaxbt46wsDBhO+PPfYb5oOnUcFJ5Egt7PRf2+jL3pYcYff6AYabc2hrJsmW3XQ4SicRkb/ob\n4JcCuUkQxoSJ3ypbt8KyZdS5wIw/D6Wh7yrBomBm1i1i79eruXwZRo+GQ4cMmVm4gwjMz3Drdsbn\nSqUSjh6FZ55B3NODMjoa1bPPMmr2AhYuhOzsL7GZVsW1se/S138Db5037zz8Dp6Onmg0Gmpra4mN\njcXDw0MQVQFIT09n/fr1rFu3DoVCIdxYGLXUe3p6mDx5MtHR0WzZsoWkpCQ+/vhjPvvsM15//XVB\nxa2hoYHMzEzmzZuHSqUiMTGRoqIiYmNjSU9PJyEhgZSUFDw8PPDx8RH2v3TpUrRaLQ0NDYKATWxs\nLGPvGYvtfFsYDtk/BrN3+nQ2bdqEUqkkLy+PxMREQZrVeNNgPE//6jzfaZuy5jLu+fQeHJVi9J81\nMmsWHF3zA0ilYGdnCOg3+w1M/Lb4JUEY04rchInfKmFh4O6OS0YWjxR3cXi6F+f1F1GJqvnqb/dz\nVubG+fMGtU9z82ymTJH8y1l240r91u02btyIRCJh27ZthD38MOLYWNizh4ILF5j27becPyMj6KEe\nqls8aZDdj0vPI7hMyELZdpk8izwc1Y54OXkRHx9Pe3s7n3/+OVKplC1btlBVVYWTkxMnTpxAp9Px\n4IMPcvXqVVxdXfH19WXy5MlMnDgRqVTK+vXreeSRR9i7dy9SqZSgoCDKy8uRyWSUlpaiVqsFD3FL\nS0tkMplguBIaGsqVK1fo6OigpqaGDz74AL1eT19fH3PmzKGjowOZTMbHH39MWVkZBQUFZBzLQF4k\nx9cBovLUzFmzhg3btmFvb8/nn39OYmIiWq0WnU5HQECAkFIPCwu7bZU80A4Vbnevk8vlHD98nOPX\nj9PRdhXbuudRlNsRfN9Vgvs0yEtLDVan8fH/RxeQibsJU2rdhInfK5GRYGeH08FjLCps58SsAMrb\nazhQt4ttb0ajqRNTUgJ5eRJGjoTQ0J+C9Z3SscbgcuvPpk+fjl6v5/7778fR0ZHUgweJ/Mc/0F26\nhKdCgadCQUBWJnMndVNp6U5ZWS8WlTNx6DmBtl9D4flC2mnnvon30VDfwIMPPkh7ezt2dnZYW1vj\n6elJfHw8FRUViMVihg4dKqxww8LC2LhxI1u3biUxMRGFQsHYsWNpbW3l7NmzPPTQQ2i1Wi5fvkxi\nYiIdHR2CfKqxNj5QJjY7O5udO3dy4MABQflt2rRpuLu7IxKJ2L9/PytXrqSvr4/S9grO5svx6BrG\nX1Ud7G5uZsrjjxMTE4NUKkWv1wujbMZzOm3aNAAhaMvlcnJzcxk3bhwqlQpPT8/bxtKM0q6TJk3i\ncPVhGvoamOM/k6qT/ri6ejJh+QgCvvwS5HKyhw5FcjO1b+K3g2n8zISJ3zOvvgpvvsnQzn52/LWa\nWKcJXOm8wv27Z/L8h9/z4ovQ2wtPPAFvvAGenoZ07s9pght/NmgUjZ9SxkJzlZcX4d98Q/bnn5Md\nEwPm5gzZs5tHS+PY7/Ed3S27GKLMZNX8D8Ecjlw/wqy3ZnHd5jp5eXmo1Wq0N11fEhMTWbt2LTqd\njpiYGPbt24dEIkEikSCTyYiNjSUiIoK8vDycnJzIyMjAz8+PiIgI3nzzTZYsWUJiYiJbt25Fr9fz\nySefAAZNdx8fHxobG2loaCA0NBSA128Krej1esaPH49arWbLli0EBgYSGxsrWJJWd9bCVOjtGE8e\n4FJayr59+4TzNHDMLjs7W9CSN6bNjQE6MDBQSKMbLVCN5/LWz2KieCIAo6adBuDLL+HL43KybxrS\nxKSnDxpHu9OYm4nfFqZAbsLE74G//Q1efhlJdx/7VpfxqOgPtF9r54Fd9zHlqW9JTTW4Yq5dq2Tu\nXDnd3T+99edm2Y2WpQMDEHCbwEzM448TsnUrXLiAat48goAHVJupZB8xza+x/eEgHhRvw9NBzMWr\nF0nYnkCLbQvV1dVERUUhkUhIS0sjLi6OmpoannjiCYKDg9myZQtg0FnPyMggOTmZUaNG4efnR3x8\nPFqtVqiTG+vtEyZMwMvLizVr1rBu3TrGjx9PRkYGSUlJZGRk4ObmxlNPPYW9vT2vvfYaXl5egrXp\nmjVrkMlkVFZWEh0dTUhICOWaMtBAv90SSmxsiNJoiAsIEBzkwKC1LhaL0Wg0t9W8jQF64HfjY7FY\nTExMjBCIlUoly5cvJ9LL0B9Q13uaOXMMAm9mZiuI2bIFhg2DggLDCOJNfq4Wbwrwvx1MgdyEid8D\nZmbIFy6E5cux7LrGjlcKSB6xgGs3rvHI7kcwj/yUzExwcBBz5Eg40dEG63NgkE3nrQx06woPDx8U\nNJYvXy4EC5VKZbBefestPI4fRx4TQz7XSeYY7/bNw3HL11j980XGjZ5Kh2UHLx1+ifqAekJCQxCJ\nRLi5uaHRaEhKSiImJoaoqChGjRqFRqNhw4YNvP/++1RWVrJ+/XpKSkoAKC8vJzY2lrVr16LVatmy\nZQsJCQn4+fmRk5PD6tWr0el0eHl5kZ6eTnJyMtXV1WRlGQxf5s2bh4uLCxqNBoVCQVlZGa6urgQG\nBiISieh36Ed7tRmcbOhRH4exY1ED1Xv2CL7jMpmMbdu2AYasQlpaGuvWrUMsFgurbWBQsDa+fmum\n4/XXX2fNmjXCivx042n+9CfDyjslRcl1OyeDXzlAcjLctIj9Of7XssAm7jpMgdyEiV8h/7bi2wDC\nJ0yAjz+GJ5/EvLOLj17MYl3Ac/TTz3MHn6PI7h3y8/sZMQJkMoPJSmXlT+83Kq3dysCVnfHxtm3b\niIuLE4LFoDT96NGEHz5M0DffoJ46lSXcIIojlDf/jYj/8iDgUiJ0wgeffEDEWxHsythFSEiI0MFu\nDNR6vZ6MjAz27t2LTCYjMDCQefPmER0dTXl5OcHBwUgkEtasMejNBwcHo1arSUtLw8fHB61Wi16v\nZ/v27RQXFwtqcW+//TZRUVF4eXkhkUiQSqUkJiayb98+tFotarUamUzGIfkh0AA3JuLrO5Xk994j\nBMiTyZCfOgUYrFoVCoWwmpZKpURERJCdnY1IJBJudvLy8oRzJxKJAAbpsovFYrZv345YLGaU6yiG\n2g6luaOZ4MmX8PcHpVLM44+vg6VLYeZMaG6GBx6Am4p1v4RpZf7rx9TsZsLEr5D/yUzwoMYpMzPD\nP/gLFzCTn2FazkW8liRzUCMjpy4HS6erbFsTww8/mAkd7ZGR4Od3exe1sRY+8PWqqioCAgIE9bJb\nj8OocpaWlsa46dMJS04me9gwpvVep6GmkkmcJ7a6inMNwXTFm1NfepEKUQVTg6eSuSOTGzdu0NbW\nxqxZs1i4cCESiYT29nZsbGwYPXo0EydOJDMzk8WLFzNx4kQ2bNjA999/j5eXF3l5eTzxxBMcOHCA\na9euERcXR1VVFQqFgr6+Pvbu3YtIJOLQoUPk5+fj6OiIhYUFQUFBvPLKK3z00UcUFhaSl5fHjBkz\nON13moKqAqiYwn0Tnuas8muaqqt5Sa9nw+XLTI+LIyAggKNHjzJ9+nQCAgKora0FDOWHgIAAPD09\nqa2txc7OjrCwMGFufOBnZvxunOEXi8Xk1OZwUXuRaT5TGSsaS1YWuLhMZ+kyc3jwQcjIgPPnUZ46\nheOjj6JUqX52IuFO3fGmmfO7D1OzmwkTvwOMK6tbU+C3pVCHDDF0SMXFgVbLU499yG7HZVgNseLj\nUx/ziuwx/uvDk8THQ2srxMQYRtJvZWBafeDvH4hcLr+jy1dgYCB5eXnI5XJili/H+0g2le+8w6Vx\nEfyFbl5sLWHbu634W/uirdMS+0ksXeFdPBD3AOvXrxfem56eLtTKt23bRnh4OMnJyVRWVlJWVkZn\nZ6dwnKNGjWLt2rX4+Pjg5eVF5c10g6urKwqFgqioKBobGwF455132LRpEwB5eXm8//77rF27Fj8/\nP5KTkxGJRHz57pc3/3Bn3NwM9qWt99zD68AaCwvhnGzatImMjAzUajX79u2jurqahISEQefReIzG\ncyUWi1m3bt1tn6MxsxEpNtTJ8xvyefJJcHKC/HyQywFXVzh4EIYORfz997By5R3T6L/U+2Di14Vp\nRW7CxG8E48rq33K+GjIEHn4YdDooKCAoW87UMbPYM7SF4qZiVEMukfZGPL09VuTnw/79cO2aIWtr\nZjZ41aZUKtHr9YjF4kFz0EbvcE9PT+RyOUePHhWEXPr7+/H19cXBwYGqqirD87AwvB5fxIWaGpZY\neXNBqeDpc6209FhyQdzHqQ9PcazzGPU/1tPc2IyFhQULFy7kzJkzfPvtt4SFheHt7c3TTz+NVCpF\no9FQWVnJ1KlTOXv2LKGhoSxevJgzZ84QGBhIWloaCxcuZOTIkYwYMQKAYcOGceLECRQKBc7Ozhw+\nfJghQ4ZQXV1NdHQ0hYWF6PV6PMWepCpS6evog7JlBAY0MXJkP6GTJvF1WhqBNTW8UVrKxHvvxdPT\nk+rqapRKJVZWVqxcuRIvLy9OnTrFnDlzhI/EeL6Mj40SrbdKrCqVSvp7+kmvSueM6gwLQ+OpOXeG\nCxckdHcbxsjldXV4/vGPhpRKQYGhCW7ixDv+LuPzf6UhYOL/X0wrchMmTNyOpSVs2AA7d4KtLTM/\nzSbvmDciGzeyL2Yze+cfeO0tDZ9+aoj7770HCxcauqRv9TM3Nm8ZR6qMrxsJDw//Wb1vDw8PVCoV\nKpWKjIwMNmVkcCNrO3EH8/jMzou9il7+eQCGLTbnnNM5Np7cyMgpI4U0dUJCAu+//z4SiYSMjAwy\nMzMRiUSCxziAj48PtbW1bNu2jejoaEpKSnjhhRfQaDTIZDJKSkrYvn07DQ0NpKenk5SURHV1NcnJ\nybi4uKDT6QRnNYC/vPUXem/0Yt7oDL2RTJ0qNfwt48fzXGAgOdevY6tWo1arWbduHYmJibS2tgIw\nb948QkJCkEqlgmb8zym9KZXK2zIfYrGYSK9Ilo5fSs+NHhbvXcz6/4rGzMzgZNvcjCHbMH06bNmC\nHOBPf4LDhwEGTRoM3Oe/4n/Tl2HiP4MpkJsw8Svg/9OGpEcfNXS3jRpFeE4FP37ej6+tJycbTzJt\n2zTuW3iJQ4cM6dvdu3/qpbqVgdadA49bqVQaUugDRqnKysqEGwCVSkVlZeWg96lUKjacyefZ4/vI\nWJXKqNZwkjf2MXw7dJt3s+KTFdS713O25KzQfKbRaMjLywMMgSw5ORknJyc0Gg0NDQ3IZDL8/PwQ\niUQ4OTmRlpZGWloaDTe7u9955x18fHxYvHgxYLBFTUlJAQw3AjKZjIyMDBoaGrDxtgHAsnckICMw\nUExISAhlpaXg7k40kGRlRUhICLGxsWRnZ7NkyRJWr17NZ599Jty4hIeH4+rq+rOB1DiHbjyPA/lo\n7keMdB6JvEnO15fX8cADhqzJm2/Kf7KnXbyY8NWrUd64AY89Br29QjOdcb//LqaU+92LKZCbMPEr\n4P/zUaHQUCgqgtmz8a+6yo8fXGWc9QgqrlQwZesUPEPL+PFHGDkSTp40dLSfP//vHbdYLBaEUIxB\ncuAqUyaTIZVKUSqVxMfHo1QqqaysZMmSJWBmRtc9Lpz/+xLGLTvEqlpXHr0MuMFm1WYWv7GYq11X\niYqKQqvVkpSUBBhGvcrKygDQarU4OTkRHBxMSUkJHh4e+Pn5kZiYSGxsLKGhoURHR5OWlkZUVBQN\nDQ1s2bKFF198keTkZFpbW4mPj6ehoUHobL+ougiNQNtIII/+fiXcuEH1unVI8/MJMTNDFBdHWVkZ\nWVlZQrnDuPKurKwUavvZ2dmDAvWsWbMEjffw8HBSU1PvuIJ2snZiW5xhtG3t8bXMXVoEKNm3L5ye\nngEbv/024sBAlBoNaX/7m9AbYNzPv8K0Er/7MdXITZgwYcDW1pA7b2nB8cRJFv2oI3/aSM71NPD5\nmc8Z4WnNhpfvJT/fnPJyJV995cjMmeDtbXi7sc5q/J6WlkZISIigLQ6GQH5rzdfbuAMMgcXR0ZHe\n3l4cHBxwcHAgNzcXLy8x81//I2esHHnqsIrAxiZyroLuehfHruXioLNnztQ5TJs2DaVSSUFBARqN\nBldXVw4fPkxgYCBtbW34+Pjw3XffkZ+fj0qlYtiwYXh7e6PRaJBIJFy5ckWor4eFhZGZmclDDz1E\nQEAAfX19fP3110RGRrKrcBc9/T2g/Bv9HT08mSjGdfUqKr//nj9YW+O4ezf9999PQUEB48aNo6Wl\nhZaWFkFjfc6cOXh6etLf38/ixYtxdHTkwIED9Pb2Mnv2bCZOnChYn8bFxZGWlsbkyZOBwf0JilMK\n3LzckF2WUXM9n2GXk6mrsSQgwHBvBhiaGurrcSwoICQykpCVK/9Hl4Wpg/3uwFQjN2HCxL+HpSV8\n8gnyl17CtceMI2vrSdL7c+3GNVYdW8WCrGl89p2C+HgxbW0wZ44hKz8Q4yrPmN4dmFI3PjeKnhhX\nm8YVqBHZzZ2KxWJWr14tvD56wmhGXT6OnziWfxRbEzUK2kRXebfyXRakLObNr/+KrttQz9ZqtQQG\nBiKVSlmxYoXQKV5WVkZiYiLBwcEA5OTksHXrVqHmHhgYKAjPREdHk56ezqpVq9BoNHh5eVFQVIBO\nrsPKx4obzWrcbZZRv2IpZQcPssLJiex33kEZGSkIyMTExCASiYiJiREmCpRKJeHh4ahUKpRKJamp\nqUilUsLDw1Gr1ULJwZjJSExMRKlUsm7dukEpbpFIxHt/eI/RFqOpuFKBVeSjQBopKYNUWuFm4xz/\nT3t3Hh9Vdfdx/BOCYZclBMKwL2oUI3VABUSNqATQqig+KgruC0Sh1SI+xQVbKKWPWlGiVVFoNbGt\nC6ItZFwwIsoiCUJQAqIomCEQAsgqW87zx829uTOZyUZ2vu/Xi1dm7ty599wT4HfPuef8zn//W66/\nDkBA4hqpnbSMqcgJqEzLlb77rvX8/MABFo44kzsH7sD/VS5NTm/CtIv/zNKZ9/Hmv3Np0cJDWhoM\nHFi0uEc4mZmZ5OXlOcHdDlbustjHyMzMZPr06cycOdPJbmYvDepLS+PUb3+k0R+e4bFu2cwdBMcO\nWN9vQENO/yWOnpE9+OeL/2Tem/NISEggKyuL/Px85/XKlSvp168fixYtYsaMGfh8PvLz84mOjmbl\nypXk5OQwaNAgUlNTuf/++4mJiSE2NpaXF77MlBVT6NPtPL77/RhmN3yWY0fXs6tZM3r95S/EX301\nEJhn3R7QZy/PGh0dTUxMDDNnzuTcc891MsHZv5usrCznfO4UuHbdBv/+vsz5kgGvDKDAFNDi7U/Y\nk3URS5bA+ecX7nDkCLRta81S+O47K8uei8/nKzaoTmqXkpYxVYtc5ARUpmfuV18NixdDhw4Mm7eW\ntXObMXrI1Rw8epAHPpzAtqGD+fWYQ+zda881L/lZqt0qtwOGPS/ana7UHay8Xi933nmnk+J06tSp\nREdHM27cOPJ37qT7/fcw4aLejL/8OWa82pbz/g0DdkFB3lG+3r6W97a+R9u/tOP1ra/z1oq3eD3l\ndacsdtrV+fPnM3jwYDIzM8nPzycuLo78/Hy6d+8OwKZNm7j//vuZPXs22dnZ5ObmsrPFTlgKpxb0\nYiZTyTy6nriOHUlas4aY/v1JT08nPT3daV3HxsaSlZXltK6XLFkCWMF91KhRThC359zn5uaSmJhY\nLOWtXS/uUed2nZ7T8Rx+f8HvMRgirrkVovZSOE7PctJJVvcJWAvQF7JzwtdUEFdWucqhFrmIlOyn\nn+CKK2D1amjThvkvP8jd389k+/7tNN7emHj+ypfP30OzZhE880wmd97pLbFl7v6stBb8pEmT6NOn\nj5On3O5iDg5kWV99RVzWOqKffI71B38ktTukNG/Itp5H4QBwEKJ2RdHuaDsem/IYTX5uwhmnn8HC\nhQu57bbbnAQs3bt3Z8mSJfTu3ZsRhet6z5kzh+7du7Np0yYmT55M5+Gdg8OOWwAAIABJREFU+anz\nT/xpcQtOzt5L08Y9aPTUg0T37OmMCA9uOQe3sqGoxe71epk2bVrAIwT3d22hrt/thy0/cM2Ca1iV\nu4qIzLto8N+X2LQJOncurOc1a+C222DoUFi4sOTfudQ6JbXIFchFJKRJkyYxY8YM683evXDjjdYz\n1qgodrz0DOOafsKb37wJQIcDQ9j67L9oFtmKBQugV6/QwcYduJOTkxkwYAB5eXnExMQ420899VQ2\nbNgABAbCOXPmMGzYMMB6hj5ixAhyc3MDvu/7z3/A5+PIa6l4f96JrznMbt+CTG9TfsnbBqcCedCq\nSSsu73M5Yy8aS/pH6fTr14+YmBiWLl1K69at2bRpE3v27GHChAnk5uaydOlSBgwYQFTLKLzjz+bI\ngaP4V8LkfV1pcetqzrvsv2zatMm5KbBHetuPEQCn637UqFFOPdiPF+yV5NzjCezrnjdvHgMGDHAe\nNwTf+LgD+9rta+n7Ul8OHzsMKf/l6bHD+e1vC3fctg1iY6FRI8jPh2bNKuFviVQXda2LiKOs04mc\nIA7QogXMn28lFjl8mLa3juPfa0/nn9e+QZsmbdja9APa/mYo+4/uYfhw+O670F33sbGxTJo0iczM\nTJKSkoiNjXW6ke0Alp6e7nT5um8G7BZrbGysE8QXLlzotIJ9Ph/xXi8rY2PZ89cnybrnHuJPas3w\n7/ay5M1tzF3XB8+X5xF7Xld279xNysEUrv/8eva02UPbtm0BSEpKYvXq1QwbNozrr7+e9PR0Fi5c\nyLhx4/hoywrOeeRcjrQ+Ss+28Mi+s8gfks0Nd+93FkMBnLXK//Wvf5Gfn09mZiZ+v5/8/Hx27dpF\namqq0yq31133+/3ExMQUS6bj8Xjo1asXsbGxAQMEIXB1NNuZ7c5k6sWFK6Bd9hDfbyooqvz27a3s\nbocOwaJFYX/vwd3dwaliRSqLEZEa8txzxjRoYAwYc+ON5ofcbNP1r10ND2BiHj7fELXXNGtmzDvv\n5DhfmTVrlvM6LS3N5OTkOK9t9raSZGRkOMeyf2ZkZDjHzMnJMRkZGc6xMz7/3ORMnmxWNG9pHgIz\nFcx0zjQT751pvH/ra4jHcDem1529zLMpzwYcNycnx8yaNcvMeiXFtLrwNEOctW/PczFXtT3TrFh6\n1MyaNcukpaWZqVOnmpEjRwacPyMjw4wZM8Y5lnu7fd12mdPS0kxGRkZAHdjfcddRuDpxO3T0kIme\n2slwN+bcW94O3HnKFOv3ds89AecZO3ZsyGOX5Xci1QMI2w2tFrmIlImzGMt998H770Pz5vDGG3S9\n9g4++fVbdOrUibzGn9P+t5ez//B+Ro/28Nln1lfsAV0+n4/4+Phio9RDPfd2f27zer0kJSU53fL2\nwilQlC3O7oLOz8+Hxo1h3DjO8W/hzGtGcjgiiiGs5Ya/TeC+BxtyVe8htDzWko0nb2T8gvF06tuJ\nU/qcAkBOjuGlRRu575+3sztuPVGd4YK3YVaHOzjnNzew8+ePGDBgAPHx8UyePJmZM2c6SWjsujr1\n1FMDutntrnF3djX31LvgxxHZ2dnExMQ4rXB3/YwbNw6fz1esqz0qMopbek0CD6xtMxXjfgw5fLj1\nc8ECZ36ax+NxFohxC5XKVaQy1fTNkYh89ZUxnTpZLbwePcy3K9KM5ymPYQqmzZh+hoYHTLNmxnz2\nWfhDBLcmQwluFYZq0Qbva7dy7f1TUlKsFm56utk0+lFzNphZVigzi85KMKP/eIU56Q8nGR7ANB7X\nxPQYc51hyJmGoRiGYjr1xPwuCnP5GWc4rfCxY8eatLQ0M3LkSKc1nZOTE/De3VtgX6v7tTFWD0BK\nSkqxVnlKSooxxhS71oceeihkvbjr89sfDhgejDVMwTwx+4miHY4dM6Z9e+t3tmZNqXUvtQcltMg1\n2E1EKm7rVmt984wMaNWKdx7/DUnH/kbuvlxrANzT82nWqDFpaTBoUOBXg+cu26OyoXgrPBT3cq2j\nRo0q1tq3W652Lnd7v2nTpjHozAHsmvQBMeufoTuHyAW2XXIhY47lsKPxd/AzMABaRjXiqrmHmJvf\nkA8eeJD48eMBq/UfHx/vjDy3p5jNnz+fQYMGsWvXroC54e5rBkLOEbffBw92s/ex6yt4wGCo8xw7\nBidd+DRmyIOc6zmPZXcutQdLWSPX586F6dPxjxmjVncdoVHrIlJ19u+3FuR4911o2JBvZj1Owp5n\nyTuQR8f9w8l5+h2aNsrH5/MUC+Y2O3CHC9p2QHPvZ4/4zs7OdqZluRPMuKdrgRV83VnljIFVHzeg\nxcyF3HnkeR7nEAnAp70uYvFpvbio7afc+O+NvH+kIa3uvpteV17pJIyJj49n3rx5tG7dmoSEhIC5\n8EDAKHwgoGt8xIgRzrXYZZ80aRKDBw9m5cqV3HbbbcyZMydgOlqohC3u64Xi3fKdeuwnZ2Q3OLaD\nD5M+5NIel1rH2bsXrrvOurOyn31IradALiJVq6AAJk2CJ58EIOvh27ngwNv83OZnOu27ip+efpPm\nTU8iLQ26dy8+Nc0d1NxTs0JlfCvpPRAQ2Ox9UlNTSUhIcKar2RneZs6cycCB1/Pc4+s4d/tcmmz9\niEcB+yl9VosWbLz7bgaMGuVMQcvOzmb16tXMmDGDcePG0bt3bzZv3sz1118fMC/dPWUuNjaWefPm\n0atXL1JTU5k+fboz7QyKzxm3s9jFxcUFZMLzeDzccsst/P3vfy/x13Hdddfh97/JFw2mQ9ffc+Gl\nF/LprZ9a9dGzp5XlraAA8vKgTZvy/a6lRmj6mYhUrQYN4P/+D158ESIjif/zq6Tn96N149b81Hw+\nnX97I/sOHGXoUNi0yUNycnKxHN4JCQlAUas8OBmKzW5hx8bGkpmZ6RwnLy/P2ccOpPaxRo0a5QyE\ni4mJcc41YcIE1q5dyMXX/cC0nA+5Y/lyfEOGkAXMadGCxBUr2BwZSXZ2Nq1bt8br9ZKQkOCsS96x\nY0dat25Nly5d8Hq9TJ482Ukuk56eTk5OTkCGtvj4eOfxgT0oLzMzk6ysrIBr9Hg8jCq8eXBnwoPQ\nWdh8Pl9Afb755pt07gx8mUTjDiezeOliFv+42LrJadnSao0XFMAHH5T2my2mOlZDc9eFlE4tchGp\nXB9+CCNHwp49ZFx0KpcM2crPR/bSde8N/PjX12jetCE+n5WbPVhqaipxcXGlrn0dPMo9+Hmyvd1u\n9bqfv0NRMJo9ezb79+9n+vTpzujxFStWMGr4cGI6dya2W7eAzG728qd2Of/1r3/RpUsXRowY4WRu\ns5PV2N3t9rN0O9+63WoHnPzv0dHRAAEtbzefz8fGjRtDPg8PZ+JEq4Pkkj9O4eNjT3BZj8v4YPQH\nVvd6Vpa1w803w2uvlfmYUnNKapHXVTU3dFBESvf118b06GEMmGVdI02LKY0MUzDdHrjZEHHUNG9u\nzOefl3wIe352MPfob/c292jvcPOf3XOy3SPNQ+0TPC89eAR68Gj0QYMGBcyPT0lJMVOnTnXmo7tH\n1Nsj0kON2k9LS3PKYI+Qd383+NrDXeszz1iD029PyjfN/9TcMAWzbMsy68NvvjFpYEx0tDFHj4b8\nvtQuaB65iFSrM86wcrOPG8d5Px5j4SuHaLwFfjj5dXr85i727S9g6FD44ovwC2ckJiY6A75CjWL3\neDzOIDKv10t6ejqA8yzcZnc5p6amOkuJ+v1+Z7lQ+/h+vz9gmVGPx4PH4yE2Nha/3+90c9ut6pUr\nVzqLowAMHDjQmUeemJhIdHS0U347b3tqaqqzjGpycrKT1S05Odm5xsTEROLj453sd+6u9KysLKen\nwWb3RgTXY7Nm1vu8zW2475z7YBk88t4j1odxccR4PFaq1hUrQtZ/ZXehV0eX/IlKgVxEqkbz5pCc\nDIsWcX7D7qR9BE2OwPcRc+h8x7XsNVsZOhQWLfKwZUvoYB4cnOyAZf9JSkpy9rFHf0NR8hXASb5i\nPxePi4vD4/EUe/acm5tLQkKC0xWenJwc0M1tJ6LJzs6me/fuDBs2jF27duH3+/H5fAwePJiYmBh8\nPh/JycnOCHn7hiArK4u4uDji4+MBK7jbr1u3bh2QhtXj8ZCXl1dsbIC9v52b3ebxeEhPTw8Iln36\nWOX+/ns/vx3wW5oMasJHeR+xausqiIjAe8011o6uNcrd9V3a443yquzjSREFchGpWhdfDGvWcNGv\n7+M/qdC4CWzp9C6RD3Rj73mjGT3+O4YP9zB/vpNszBH8rNgOivYfO9DaAW/GjBnOd+zR68GD57Kz\ns/H7/c5AM7t1bs81nzdvHl6vl927dwNWi96d/z06OppNmzaRl5fnPAvPz88nMTHRWcAlKSmJzMxM\n52bB7/ezaNEivF4vMwvXF7WDrz2wLT093QnU9nftmw+Px+Osy+5u9duB2+fzER0dHRDgO3e26iw3\n10O7Zu24t9+9AEz7rDB3+uWXWz9dgVxzyusmBXIRqXrNm8NzzzH41U9YltaREevgWIPDMOh1uP9U\n1p52I1ffs5r+/eHjj62vlJQUJjitq91VbQfo/Pz8gP0Ap/vabpEHB/jo6GhnkRKAfv36OS13e93w\npKQk4uPj6d69O4mJicyZM4fMzExnIN38+fOd0fSxsbHODUZ6ejqDBw8G4OSTTw64NruMcXFxAM6N\nhZvP53NGytsD4pKTk52blfj4eGJiYvD7/c7NQ7t21jLk+flw8CD8buDvaBTZiLfXvc3X27/Gf8op\n0KQJfPUV5OQ459Ia4VJdanrcgYiEUdoiH2bfPmPGjzfftMXcehWm4WMYphT+GTXc0GWxueQSY5Yt\nK0pTGk5GRkaxwW/BA8GCB4O5B5sFH8suv3uRl6lTpxZLqWqnU3W7/PLLwy5yYg94C/7MLp+7nMEp\nWu2ylbaAiXtQnK1bN2vA24YN1vtx/xlnmIIZ9fYoa8MVV1g7vPxyicd2X6sWUqkZlDDYra6q6ToV\nkUIV+Y89IyPDmE8/NaZnT7P5ZMyEYRGm8YMnFQX02883nPq+Oe+8hWbNmqL85Pa53EE34JiF7Hzk\n7u2hyuleNS34BsAdSO1R58F50t3HycjIcEapu/dxj0K3bwpClcU+Z/Dx7W2l3iCFcMEFVpz++GPr\n/Y+7fzQN/9DQNHiigdmwY4MxL7xg7XDttQHlcP+U2gEFchGplfbtMyYpyRgweU0xj01PNK2mty4K\n6GPjDWe9bs7uO9Ns3Fj+w4dqARtTtFSpO+Dbn9vBPS0tzTz00EMhg+jYsWND3iDY0+WC9586dapz\nYzB27Nhii6i4hWv9uqfBuT9z9w4EB+FRo4yBHDN3btHx75h/h+FuzK3v3mpSHnrICuSXXWaqkm4K\njh8K5CJSmSq91fbUU1ZAAbPn0YfMU58/aWL/4ikK6BO6mQbnJZuZzx8o9lV3y9kOoO5tJZUx3Api\ndnC0W8/ubuvgwB4cyO1Weah54+755MHfD1fO4GsJbrGXdH3jxuUYMGbixKJ9NuZvNBEPRpjIJyLN\nptTnrXofMSLsMaR2QIFcRGq9OXOMiYy0Asu4ceaXQwfM7IzZJvqm9kUB/XftzJA//MnsOrA74Kvu\n4GYHvuBueGOKkszY3d3uFro7oLqTuLi7woN/2i1wexlSO+gHt6qDu+9DtfLd57F7DNzHCe6SL6kl\nb3vxRWMgw4weHbj95nduNtyNuefJBJMDptgO1agijwxORCiQi0h1q1Br/d13jWnUyArmN9xgzKFD\n5uixo+bNr980XaZ6nYDe+LE25r3s9wO+Gtz1XFbu7vDgIG4fzz5mcIvaXus8+Nzu7HKzZs0KeKYf\nnCnOmOJ1dckll4S9nuDscSV59dUMA8Z4vUXlNcaYdXnrTMSUCHPSlEjzcyOMGTu29IqSGoUCuYiE\nU+ueX37yiTEtWljBfOhQY/btMzk5OaagoMD8/pUPTMTtFzgBfaJvkjly7EixgFbaNdkt52DBgTXU\nqHj79ZgxY0Ie233ctLQ0M2bMmICgHBz8jTHOPu4/wed3C9WiD66DWbNmmV27rGps0sSYLVuKyv/d\nzu9MxJQI02hKQ7MnCmMmTnSuq9b9fRBjjAK5iNQ1K1ca07atFYUGDjRm504nwCxYeMyclDDD8Fik\n4W7M+bMvMDl7cop1Q5cm3LNqdx704Clg9sj04O+Fmo4W6tihRseHepYeaiR9cA74cCPo3WUyxhiP\nx+petwcLZmRkmEkfTjJMwYx+LN6q4yeeCFv20q5JqgfKtS4ix6Pak4T07QtLlkCXLlZC9gsvJHft\nWgCGDW1A+rSHaP72ImjRgc9/+oxf/e1sdrfeXa5yBq91bucvtxOzeL1e57W9XrrX66Vfv34AAelU\nExMTnVXWQsnNzcXn85Gbm+usimZvtzO12Rne7Guws9fZ7EQw7s/CpT11p6Dt3Rsglq+/tj7Lyc3h\nlVWvAHDv/tOtjS1aONcJZft9Kwtc7aFALiKlqpH/tE87zQrmcXGwdi3ee++F774DrCVQP0+9kJh3\nVsH3g8k7sJ3L/nEZr3z7CgWmoFgucjd3rnZbXl5eQCC207fai5p4vV4ne5udRtXOpOY+jr2Pe5ud\nqc0O9u5jeL3egEVR7AVR7PSz9jb3oipZWVlhr80uu5sVyD1OIN/beS87DuzgrPZnMeDnwgBemAnP\nzhSnIC3VoaZ7OUROKJXVjVregWjGGGPy8ozp18/qAo6NNWb1auejjRuN6XXqUcPFjxoejzA8gEmY\nnWi279t+/Od1Ce7OTklJMSNHjiyWUCbc8+zg0eju44YqY/B0t+DjhEtuE6rcL79sVd1NN1nbLnjV\nGmMwfcF0a0AhGJOaGrJMZaEu9uqBnpGLSJ22Z48xgwdbQadlS2OWLHE+OnDAmMcfN+ak0xcaHoo2\n3IRp+URH8+mmz4tlaAsOOsGpWN2vwz2jDp6rHu7ZvDujW7j56vZ+7qxuwSlig4/rvpZQaVmDffGF\nVW2/+pUxWduyDFMwzf/U3Oz5ZY8xl19uffjee2HLKbUDCuQiUleEDSYHD1qJS+xh2AsWBAS4jRuN\nufjqzYbbB1qj2h9raJJef9IUFBSUfNwSyhAu+5o7QAePLHfPAQ83hzz4BiNU3vbg84aajhacmS7U\nvrt3W1UWFZVhkv5zn2EKpt9N/awdL7rIpIExixaF/L7UHiiQi0hdUeLc6CNHjLnjDisyNWxozO23\nB3S1FxQY8/a7h83JIx9wpqh1nni1WbziG2NMURd5uCQk4ZKshOsyd38v3D7hppDZZQhumQf3AgSn\nYg2Xpz2YewR8p07GELXXNJ92suEBzAerPrB26tvXSgizYkXIc0rtgQK5iNQlwV3LAQoKjHn4YSel\nqwFjEhKMmTfPmKNHjTFWd/v/PPaO4eGWhimYiN92N2OnLDRHjliHCPc8uTShpooZU/LCLMHbg59z\nh8qt7k72UtKz8dLStdrvvd40w5l/MUzBDJg9oOh7p51mBfJvvinxum2lJaApqWxyfCghkEdUY/Ct\nTIXXJSInrA0b4LnnYO5c2LfP2ta9O9x/P9x+O7RsycervuOaN65jT7NVcDSKTmtn8s/f3cP554f+\nr8+9xnmwzMxMvF5vwD72yPKsrCw2btzorGVuj0R372tPYRs1apRzLLCmscXExBAbG0tWVhbx8fGl\njhoPVU6fzxcwAt59jptuziC1+V3QYRX/uPofjO4z2tqpUydrLfLNm/FHRmq0ei0WEREBdTdmh1TT\nN0ciUlvs3m3M008b0717UQu9eXNj7rvPmA0bzIHDB03ic/cabirM137NKHPz7XvNtm2hDxduYFpJ\nXdp213q4LvuydM27E9K4u+qDv1uWru/gzyc/v9wwBRP1aBtz8MjBon1atrTqy5VwR2on1LUuIvXe\n0aNWrvaLLw7sdh8+3Bifzzy14Dlz0uPNrGB+a0/Tosdak5zs9MaHFKr727093PuyCnVcdxAPd/7g\n85bW5X35y7cabsLE3PRg0caCAmeRmoxlyypUfqk+KLObiNQ3wYlPiIyEq66CRYvIfOMNq3u9USNY\nsAASE3ngdy+wOuZ39GpxOnT7jr03nEvSi69xzjmwdGnRYdzJXOyuZq/XG5D1LDc3l+TkZOe9x+Mp\nXh7X8fx+f8gkLtnZ2QHHtTO25eXlBRzPfX73drt8dnd9cP2kpqay6+AuPsxMhVNg98f3cOxY4Q6H\nDsGxYxAVhfe880KWW6Qq1fTNkYjUUgGt1+3bjZk61U44bgyYfTGtzOjJvQ13Y/359Z2GhgfMgAEp\nZu5cYzIzjfnll+Mvh7uVHpyfPdQ+xpS+pKe7xe5utZfUI/DXpX+1Voy761IDxqxfX5hH/oUXrDpp\n06bCK8eFK6NUPjTYTUROaEeOwFtvwcyZsHw5BngqHh4Z0YBDDQogtw/8+03YeQpgNe7j4uCss6BP\nH+tnu3Z+YmNh27ZcYmNjnTSqpQ0Qcw86g9CD0uxBcPZ7wPlO8OC64PNlZmYSGxtLenq6cwx7AF37\n9u25ZN4lrF+2nh5bHuH7xX/knXdgxAjghx+swYFdusCPP4Ysa1m4879L1SlpsJsCuYicWJYtswL6\nW2/xVdujjPwf+G4DNOoUxTnH/s7WxRfy/fdgjAfIBIoCW3S0FdT79oUHHoAOHUIH17Jus7dD+EAY\nLriGO577RuGTTZ8w+B+D8bTwMHzDF8x+sSt//CM88giwdi3Ex8MZZ2AnYq9IIJfqUVIg1zNyETmx\n9O9P6q9/DT/8wK9u/z0Zb7bm2pPhUKfDLOl6I1eMvpadG47x5Zcwe7aX8eMhIQFat4b8fPjkk0ye\nfNJP377wzDM+5/l4qGfrbuECtcfjYd68ecUWYAErWNsLmUCIcQGFkpOTnWfw9oIsAC+sfAGAMb3v\n5Os1XQGfM1PPedG8ubO/gnjdpBa5iJwwQrY4Dx7EpKTw7ILH+N2ZWzkaCefmRPCn3X1p3703/kZt\nSbjiWk464yxydjdjzRqYMQMWL7bG0s2Y4WfChOLd3RXpoi6te9rn85Vpnnlqaiptu7RlWMowjDH0\n/2EzS30N6NzZ46wOy0cfwWWX4TvrLBJXry5zGaRmqGtdRCQMJ3gZw7L3nud/VkxkS9TBwJ32QItG\n0LagMY2Peojp0oWt/o58uzoaftrFpZefz/+cH0VC/CC+X/99wDPwkOcKI/gGwN5/0qRJzJgxo8Tr\n8Pl85OfnO8/Jx80exws5L9Bu59Vsf3YeHTrACy9kctVVhcd/7TUYMwauvBLmzy+1nsrbxV/aZ1I+\nCuQiIi4lBZj8A/k88v5vWLs5gx0H8sg/upcd2w5hOhbu8C1wAOgT9MU9EHFyBKe1PY3TG51OfLt4\nLj7rYs6OPZuWjVsC5Wup213liYmJxQbElWTatGk0HdyUSR9N4kjBEXh6JG0azmTJEg+rVqVax/j6\na7jgAti1i6KH5uEpINc8BXIRkeNQYAr4OW8L+VMns2NeCvlN4J8RzTh78mhWFbThzbQcDrVaDe3W\nQuTRYt/v1aYX53Y8l3M859C/U3/aF7Rn145dJQb1cClXSxrk5h3k5db5t7Lg2wXWxmXjabX8GdI/\niSA3t/B4mzfDwIFWatYrr4S334aGDY+/kqRKKZCLiFRAyKC5dCncdZcz0pvbbmPL+P/jytui+Wrt\nL1Yw75BJs1My4Ngifum9mWMctvZdDfSBqMgoeuT3YNjQYQzoNID+nfrTuWXnMpXF/pmcnExSUhJH\njkBWFry2ZBEv7biZA5Fb4WBrmP8qJ/uv5uOPoV+/woPs2GG1xLOzYdAg+OADaNKkUuusPOxrkNIp\nkIuIlKC8Xce+//yHxK++srqlDx+GmBh+mTGTBSffwIsvRfDZZz4OHixsTTc4Au2+pmHXFbSJX86x\nDsvIj/ym6GB7rB8dO3akf6f+nNHoDIZ6h+Lt4KVxw8YBZTt2DNavhy+/tP6sXAmr1hzh8MDHYdCf\nIcLAjxcQMS+F3p0ieeklD127FmaeW7IE74MPkrliBbFxcXiWLoVWrSqrCgOoK77yKZCLSL2Xmppa\npmfIZRHc+g1r/Xq45x749FPr/bBh8PzzFHTpxrp1VuP9tddSycsbxbp1AKnAKGi8GzquoOWZS2ly\nylJ+brGcgzm7wXWqhvsa0rurlw4F/Yn0D2DHV/1Z+3lX9u+z/9vOhFZt4NoboeUyIlo0YEjjR+m3\nvyf/+/BomjVzlfPwYfyXXYZn8WLo1g2++MKaBF8ouBu/NO5n/ZVZ7xKeArmI1HmlZTizlTcolXQ+\nKEPGsoICePVVmDgRdu+Gpk3xT5yI59FHrRRxhXbuhOXL4bXXfOTlJbJ8OezdC5AKETdA9Hoadl9G\ndJ+l7G+9jH1N11otbNvbwJBYmuT3p2ejAfTqfDIfmofZf+xnWm1oxbvT3uWibheFLt/NN8Mbb0BM\nDP533sEzaFDAdYa6xtIG5il5TPVSIBcRKVRZAajYcXJz8d99N5733wcgtVs3oidOhJ49nZHn7rSr\nx45ZS6qvXAnr1nn48EMffn88TrO80R5a9V5BO+8yDjZIY3fndezN3gmnuArhhysvvpJXr3yV6KbR\nxctkDEyYYK3b3qIFpKeD11vmZ9PqIq89FMhFRKqJf+5cPI8+iu+nn0iMjIQHH4THH4emTcN/pzBg\n5udbGWRzc/1cdpmHzp0hovB/6bS0NHqc04OlW5ay7KdlbNi5gUvbXsqQ9kPo27dvQBe3E4CnTbOm\nlkVFwcKFMHhw2DKEGyVf4rUq0FebkgJ5XVVtK86ISP1QHatyOauH7dljzPjxxkREmBwwpkcPYz78\nsNLOU6ZrefFFa3WziAhj3nqr2HdLOkbweui20tY9l6qDVj8TEak6YVumy5fDXXfhz8qyOszHjIGn\nnoK2bUvt3q7oIisAvPMOXHed9Xz8b3+zBuSVk56B1y7qWheReqm6gk15U6sGbI+PhyefxD9lCp7D\nh0lu0oSkiROZlpPD5FtugQYNrP7ziIiQr33LlpF4/vmBn4f6ToNHfXAJAAAJQklEQVQG+Ldvx7Nj\nB1x7LRw+TOa99+J94YUSrys3N7fUOiwtGU1FqFu+fBTIRUSqiDsglXhj8e23ZI4ahXflSvwEzDQr\nl8CFVUtw333w7LNFD9lDlDeUyhr1X141dd66QoFcRKSKlamFaYw1DWzdOmvueUGBtc3+6X59PNuu\nucbqwm9QvpWq1UquvRTIRUTKoDK66ssSDCt6nuMNtOU5b6hzBW+zW9F6nl71Sgrk5btdExGpx6oq\nGKWmplboPJmZmQHvwwXx5OTksMewB8eV57zhzhW8ze4KD3dc97ml6qhFLiJSS9ktYJ/PR0xMzHG1\npqVuU4tcROQ4BbeOy6O0lmm4Y9vBODEx8bhb0yWpjJazWt81R4FcRKQMyhJI7WBW1i5x97ErEgiP\n5+bCVhmtd5/PV+Ixgq9NQb9y1UTX+lDgGSASmA3MCPr8JuAhrLLtBcYCa4L2Ude6iNSImui2PlG6\nyjVoLrza1LUeCczCCuZnADcCpwft8z1wIXAW8EfgpeosoIhISTweT7HBa6FUZquzurvK3d/3+XzF\nPg+1rTIoiFdMdbfIBwCPYwVygIcLf/45zP6tgSygU9B2tchFRMqgLK35ymzxl3VlNSmf2tQi7whs\ncb3/qXBbOHcAC6q0RCIiFVRZre7KeNYdTlkCdLh9KnJ9SUlJAd+rymsTS8NqPl95mtEXA7cD54f6\ncMqUKc7rhIQEEhISjqdcIlKPVdWz18pqxVZW2cK1rCua/rSi1+f+Xrhry8zMJDY29oR49l8R6enp\npKenl2nf6u5a7w9Moahr/X+BAooPeDsLeKdwv40hjqOudRGpUZV5c1CRru3ynL+mBpG510iX41Ob\nutZXAqcA3YAo4HrgvaB9umAF8ZsJHcRFRKrUpEmTSt2nMgNjRVql5Tl/afuG60K3B/VVdHCbgnj1\nqInpZ8Momn72CjAdsBfLfRFrStoIYHPhtiPAuUHHUItcROqcqppGVhnHPVGmuNVVWjRFRKQK1ZUg\nWBuWCnV389eVeqsNFMhFRGqJmg5e1RnMa/pa65Pa9IxcRKRGlbRSWHWo6sB23XXXlfh5WYN4aVPP\nyjI1rbKvValdQ1OLXESklrG7n9WiFZta5CIilaC6kpvYz5DLEsTre8KVsswgONEpkIuIlFFtzAWe\nl5dXbFtVLrla3WbMCE4zIsHUtS4iUstVRRd7feq2rw2j8auaRq2LiEitUp9uJKqDnpGLiEi1qW3d\n8/WdArmISC1Wm4Ji8Drs4cp2PCuuSfmpa11ERCpE3ePVR13rI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6e73863cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
    "plot_MCMC_trace(ax, xdata, ydata, emcee_trace, True,\n",
    "                colors='blue', linewidths=2)\n",
    "plot_MCMC_trace(ax, xdata, ydata, pymc_trace,\n",
    "                colors='red', linewidths=2)\n",
    "plot_MCMC_trace(ax, xdata, ydata, pystan_trace,\n",
    "                colors='green', linewidths=2)\n",
    "ax.legend(ax.collections[::2], ['emcee', 'pymc', 'pystan'], fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如我所料，结果都差不多！这表明我们定义的模型在这三个包都一致。另外，我们看到用来产生分布的“真”值(25, 0.5)落在1-$\\sigma$的椭圆区域内。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 三个包比较"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "哪个包好？因地制宜。下表是我自己的总结：\n",
    "\n",
    "<table>\n",
    "<tr>\n",
    "<th></th>\n",
    "<th>复杂性</th>\n",
    "<th>执行时间(100,000样本，包括准备阶段)</th>\n",
    "<th>安装简易性</th>\n",
    "<th>使用友好程度</th>\n",
    "<th>特性丰富程度</th>\n",
    "</tr>\n",
    "\n",
    "<tr>\n",
    "<th>emcee</th>\n",
    "<td bgcolor='#CCFFCC'>轻量版</td>\n",
    "<td bgcolor='#CCFFCC'>~6秒</td>\n",
    "<td bgcolor='#CCFFCC'>纯Python；pip安装简单</td>\n",
    "<td bgcolor='#CCFFCC'>直截了当 & Pythonic</td>\n",
    "<td bgcolor='#FFCCCC'>除了MCMC取样没太多功能</td>\n",
    "</tr>\n",
    "\n",
    "<tr>\n",
    "<th>pymc2</th>\n",
    "<td bgcolor='#FFFFCC'>大量功能 & 选项</td>\n",
    "<td bgcolor=\"#FFCCCC\">~17秒</td>\n",
    "<td bgcolor=\"#EEFFCC\">要求fortran编译器; 可通过conda编译</td>\n",
    "<td bgcolor=\"#FFFFCC\">Pythonic，但有大量的pymc引用文件</td>\n",
    "<td bgcolor='#CCFFCC'>大量的内建Python功能</td>\n",
    "</tr>\n",
    "\n",
    "<tr>\n",
    "<th>pystan</th>\n",
    "<td bgcolor='#FFCCCC'>很多包; 要求Stan语言编写</td>\n",
    "<td bgcolor=\"#FFFFCC\">~20秒编译 + ~6秒计算</td>\n",
    "<td bgcolor=\"#FFCCCC\">要求C编译器 + Stan安装; 没有编译好的文件</td>\n",
    "<td bgcolor=\"#FFCCCC\">不是纯Python; 必须学习Stan建模语言</td>\n",
    "<td bgcolor='#EEFFCC'>大量Stan功能</td>\n",
    "</tr>\n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "啰嗦几句：\n",
    "\n",
    "**emcee**可谓短小精悍。你要做的所有工作就是Python对数后验，之后emcee就会从分布取样了。因为是纯Python而且没有许多常见的分布(如均匀分布，正态分布等)。我觉得它可能比另两个包慢，但是性能差的并不多。可能是取样算法相对简单，所以跑分不差。\n",
    "\n",
    "**pymc**功能全面，一旦你明白了修饰器语法，分布函数，派生变量(derived quantities)，那么还是容易用的。它的性能比其他两个都差：同样的查询花更多时间，尽管不同的先验取样都优化过。听说PyMC 3是完全重写，还是值得期待的。\n",
    "\n",
    "**pystan**是最难用的，但那是因为不是真Python包。模型也不是Python的，是一种统计语言。这种语言很给力，但是有点难学。约20秒编译时间挺烦人，但我认为随着样本增大模型会更复杂，这点儿可以忽略。Stan是为这种工作设计的，模型都被编译成字节码，在做大case的时候是个不错的选择。\n",
    "\n",
    "这里就不花太多时间了；前面说过，这些包用了不同的取样算法所以时间是不可比的。每种取样算法都有优缺点，你可以去看看。\n",
    "\n",
    "希望我的比较是公正合理的。当然我不是这些包的大牛；只是简单读了一些文档，然后把教程的例子改改罢了。如果大牛碰巧读了这些，轻喷哈。再说两件事：\n",
    "\n",
    "1. 如果你用的更好，写点儿评论哈！\n",
    "2. 提醒一下那些*想用这包解决问题的一般用户*：读读教程，因地制宜。\n",
    "\n",
    "感谢御览！\n",
    "\n",
    "<small>\n",
    "这篇博客是IPython notebook写的。可以[下载](http://jakevdp.github.io/downloads/notebooks/FreqBayes4.ipynb)，或者看[nbviewer](http://nbviewer.ipython.org/url/jakevdp.github.io/downloads/notebooks/FreqBayes4.ipynb)静态网页。\n",
    "十分感谢David W. Hogg对本文提出的建议。\n",
    "</small>"
   ]
  }
 ],
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